66 results on '"Jaan Oitmaa"'
Search Results
2. Magnetic phases in the J1−J2 Heisenberg antiferromagnet on the triangular lattice
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Jaan Oitmaa
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Physics ,Condensed matter physics ,Magnon ,Phase (matter) ,Excitation spectra ,Order (ring theory) ,Antiferromagnetism ,Condensed Matter::Strongly Correlated Electrons ,Hexagonal lattice ,Series expansion ,Phase diagram - Abstract
We use series expansion methods to investigate the phase diagram of a spin-1/2 Heisenberg antiferromagnet on the triangular lattice with first- and second-neighbor interactions. We find regions of ${120}^{\ensuremath{\circ}}$ and collinear ``stripe'' order, separated by an intermediate nonmagnetic phase, in agreement with results obtained previously using other methods. Magnon excitation spectra in the ordered phases are also obtained, and discussed.
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- 2020
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3. Frustrated diamond lattice antiferromagnet
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Jaan Oitmaa
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Physics ,Condensed matter physics ,A diamond ,02 engineering and technology ,021001 nanoscience & nanotechnology ,01 natural sciences ,Tetragonal crystal system ,Lattice (order) ,0103 physical sciences ,Antiferromagnetism ,Condensed Matter::Strongly Correlated Electrons ,Wave vector ,Diamond cubic ,010306 general physics ,0210 nano-technology ,Series expansion ,Phase diagram - Abstract
We use series expansion methods to investigate the phase diagram of a spin-1/2 Heisenberg antiferromagnet on a diamond lattice with first- and second-neighbor interactions. Using series expansions at $T=0$, we find an apparent second-order transition from collinear N\'eel order to an incommensurate spiral with wave vector $(k,k,0)$ at ${J}_{2}/{J}_{1}\ensuremath{\sim}0.18$, considerably higher than the classical value $\frac{1}{8}$. We extend the calculation to the case of tetragonal distortion, as occurs in the material ${\mathrm{CuRh}}_{2}{\mathrm{O}}_{4}$. Here we find a clear second-order transition from N\'eel order to a $(0,0,k)$ spiral.
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- 2019
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4. Properties of the spin-liquid phase in the vicinity of the Lifshitz transition from Néel to spin-spiral state in frustrated magnets
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Yaroslav A. Kharkov, Oleg P. Sushkov, and Jaan Oitmaa
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Physics ,Condensed matter physics ,02 engineering and technology ,021001 nanoscience & nanotechnology ,01 natural sciences ,Square lattice ,3. Good health ,Phase (matter) ,0103 physical sciences ,Antiferromagnetism ,Condensed Matter::Strongly Correlated Electrons ,Field theory (psychology) ,Quantum spin liquid ,010306 general physics ,0210 nano-technology ,Series expansion ,Spin-½ ,Phase diagram - Abstract
Three decades ago Ioffe and Larkin pointed out a generic mechanism for the formation of a gapped spin liquid. In the case when a classical two-dimensional (2D) frustrated Heisenberg magnet undergoes a Lifshitz transition between a collinear N\'eel phase and a spin spiral phase, quantum effects usually lead to the development of a spin-liquid phase sandwiched between the N\'eel and spin spiral phases. In the present work, using field theory techniques, we study properties of this universal spin liquid phase. We examine the phase diagram near the Lifshitz point and calculate the positions of critical points, excitation spectra, and spin-spin correlations functions. We argue that the spin liquid in the vicinity of 2D Lifshitz point (LP) is similar to the gapped Haldane phase in integer-spin 1D chains. We also consider a specific example of a frustrated system with the spiral-N\'eel LP, the $J_1-J_3$ antiferromagnet on the square lattice that manifests the spin liquid behavior. We present numerical series expansion calculations for this model and compare results of the calculations with predictions of the developed field theory.
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- 2018
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5. Quantum Spin Ice with Frustrated Transverse Exchange: From a π-Flux Phase to a Nematic Quantum Spin Liquid
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Rajiv R. P. Singh, Jaan Oitmaa, Nic Shannon, Owen Benton, Ludovic D. C. Jaubert, Condensed Matter Theory Laboratory RIKEN (RIKEN), RIKEN - Institute of Physical and Chemical Research [Japon] (RIKEN), Laboratoire Ondes et Matière d'Aquitaine (LOMA), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), University of California [Davis] (UC Davis), University of California, University of New South Wales [Sydney] (UNSW), Okinawa Institute of Science and Technology, Okinawa Institute of Science and Technology Graduate University (OIST), Theory of Quantum Matter Unit of the Okinawa Institute of Science and Technology Graduate University, IdEx Bordeaux BIS–Helpdesk, and USA National Science Foundation Grant No. DMR–1306048
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General Physics ,Pyrochlore ,FOS: Physical sciences ,General Physics and Astronomy ,02 engineering and technology ,engineering.material ,01 natural sciences ,Mathematical Sciences ,Condensed Matter - Strongly Correlated Electrons ,Engineering ,Liquid crystal ,Phase (matter) ,0103 physical sciences ,[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] ,010306 general physics ,Quantum ,Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Condensed matter physics ,021001 nanoscience & nanotechnology ,3. Good health ,Physical Sciences ,engineering ,Ising model ,Condensed Matter::Strongly Correlated Electrons ,cond-mat.str-el ,[PHYS.COND.CM-SCE]Physics [physics]/Condensed Matter [cond-mat]/Strongly Correlated Electrons [cond-mat.str-el] ,Quantum spin liquid ,0210 nano-technology ,Ground state ,Series expansion - Abstract
Quantum spin ice materials, pyrochlore magnets with competing Ising and transverse exchange interactions, have been widely discussed as candidates for a quantum spin-liquid ground state. Here, motivated by quantum chemical calculations for Pr pyrochlores, we present the results of a study for frustrated transverse exchange. Using a combination of variational calculations, exact diagonalisation, numerical linked-cluster and series expansions, we find that the previously-studied U(1) quantum spin liquid, in its pi-flux phase, transforms into a nematic quantum spin liquid at a high-symmetry, SU(2) point., 5 pages in main text, 10 pages supplemental material
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- 2018
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6. Incipient and well-developed entropy plateaus in spin-S Kitaev models
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Jaan Oitmaa, Akihisa Koga, and Rajiv R. P. Singh
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Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Fluids & Plasmas ,FOS: Physical sciences ,02 engineering and technology ,021001 nanoscience & nanotechnology ,01 natural sciences ,Heat capacity ,Binary entropy function ,Condensed Matter - Strongly Correlated Electrons ,Entropy (classical thermodynamics) ,Engineering ,Quantum state ,0103 physical sciences ,Physical Sciences ,Chemical Sciences ,Condensed Matter::Strongly Correlated Electrons ,cond-mat.str-el ,010306 general physics ,0210 nano-technology ,Anisotropy ,Series expansion ,Mathematical physics - Abstract
We present results on entropy and heat-capacity of the spin-S honeycomb-lattice Kitaev models using high-temperature series expansions and thermal pure quantum (TPQ) state methods. We study models with anisotropic couplings $J_z=1\ge J_x=J_y$ for spin values 1/2, 1, 3/2, and 2. We show that for $S>1/2$, any anisotropy leads to well developed plateaus in the entropy function at an entropy value of $\frac{1}{2}\ln{2}$, independent of $S$. However, in the absence of anisotropy, there is an incipient entropy plateau at $S_{max}/2$, where $S_{max}$ is the infinite temperature entropy of the system. We discuss possible underlying microscopic reasons for the origin and implications of these entropy plateaus., 6 pages and 11 figures
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- 2018
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7. Competing orders in spin-1 andspin−32XXZ kagome antiferromagnets: A series expansion study
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Jaan Oitmaa and Rajiv R. P. Singh
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Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Condensed matter physics ,Sixth order ,Heisenberg model ,FOS: Physical sciences ,01 natural sciences ,010305 fluids & plasmas ,Condensed Matter - Strongly Correlated Electrons ,Magnetization ,symbols.namesake ,0103 physical sciences ,symbols ,Condensed Matter::Strongly Correlated Electrons ,010306 general physics ,Anisotropy ,Hamiltonian (quantum mechanics) ,Series expansion ,Ground state ,Phase diagram - Abstract
We study the competition between $\sqrt{3} \times \sqrt{3}$ (RT3) and $q=0$ (Q0) magnetic orders in spin-one and spin-$3/2$ Kagome-lattice XXZ antiferromagnets with varying XY anisotropy parameter $\Delta$, using series expansion methods. The Hamiltonian is split into two parts: an $H_0$ which favors the classical order in the desired pattern and an $H_1$, which is treated in perturbation theory by a series expansion. We find that the ground state energy series for the RT3 and Q0 phases are identical up to sixth order in the expansion, but ultimately a selection occurs, which depends on spin and the anisotropy $\Delta$. Results for ground state energy and the magnetization are presented. These results are compared with recent spin-wave theory and coupled-cluster calculations. The series results for the phase diagram are close to the predictions of spin-wave theory. For the spin-one model at the Heisenberg point ($\Delta=1$), our results are consistent with a vanishing order parameter, that is an absence of a magnetically ordered phase. We also develop series expansions for the ground state energy of the spin-one Heisenberg model in the trimerized phase. We find that the ground state energy in this phase is lower than those of magnetically ordered ones, supporting the existence of a spontaneously trimerized phase in this model., Comment: 5 pages, 1 figure
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- 2016
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8. Diamond lattice Heisenberg antiferromagnet
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Jaan Oitmaa
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Physics ,Condensed matter physics ,Magnon ,02 engineering and technology ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,01 natural sciences ,Renormalization ,Magnetization ,0103 physical sciences ,Antiferromagnetism ,Condensed Matter::Strongly Correlated Electrons ,General Materials Science ,Diamond cubic ,010306 general physics ,0210 nano-technology ,Spin (physics) ,Series expansion ,Quantum - Abstract
We investigate ground-state and high-temperature properties of the nearest-neighbour Heisenberg antiferromagnet on the three-dimensional diamond lattice, using series expansion methods. The ground-state energy and magnetization, as well as the magnon spectrum, are calculated and found to be in good agreement with first-order spin-wave theory, with a quantum renormalization factor of about 1.13. High-temperature series are derived for the free energy, and physical and staggered susceptibilities for spin S = 1/2, 1 and 3/2, and analysed to obtain the corresponding Curie and Néel temperatures.
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- 2018
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9. Phase diagram of the Heisenberg-Kitaev model atT=0
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Jaan Oitmaa
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Physics ,Work (thermodynamics) ,Phase (waves) ,Order (group theory) ,Statistical physics ,Condensed Matter Physics ,Series expansion ,Ground state ,Electronic, Optical and Magnetic Materials ,Phase diagram - Abstract
We use series expansions to investigate the zero-temperature phase diagram of the Heisenberg-Kitaev model. Our work confirms the presence of four distinct magnetically ordered phases, identified in recent work, and provides accurate values of the ground state energy and order parameter throughout. We call into question the previous estimates of the location of phase boundaries, and provide an analytic argument for their location.
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- 2015
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10. Magnons and excitation continuum in XXZ triangular antiferromagnetic model: Application toBa3CoSb2O9
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Adolfo E. Trumper, Jaan Oitmaa, E. A. Ghioldi, Luis O. Manuel, A. Mezio, and Rajiv R. P. Singh
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Physics ,Condensed matter physics ,Heisenberg model ,Magnon ,Condensed Matter Physics ,Electronic, Optical and Magnetic Materials ,Brillouin zone ,Mean field theory ,Spin wave ,Quantum mechanics ,Condensed Matter::Strongly Correlated Electrons ,Continuum (set theory) ,Series expansion ,Boson - Abstract
We investigate the excitation spectrum of the triangular-lattice antiferromagnetic XXZ model using series expansion and mean field Schwinger boson approaches. The single-magnon spectrum computed with series expansion exhibits rotonic minima at the middle points of the edges of the Brillouin zone, for all values of the anisotropy parameter in the range $0\ensuremath{\le}{J}^{z}/J\ensuremath{\le}1$. Based on the good agreement with series expansion for the single-magnon spectrum, we compute the full dynamical magnetic structure factor within the mean field Schwinger boson approach to investigate the relevance of the XXZ model for the description of the unusual spectrum found recently in ${\text{Ba}}_{3}{\text{CoSb}}_{2}{\text{O}}_{9}$. In particular, we obtain an extended continuum above the spin wave excitations, which is further enhanced and brought closer to those observed in ${\text{Ba}}_{3}{\text{CoSb}}_{2}{\text{O}}_{9}$ with the addition of a second neighbor exchange interaction approximately $15%$ of the nearest-neighbor value. Our results support the idea that excitation continuum with substantial spectral-weight are generically present in two-dimensional frustrated spin systems and fractionalization in terms of bosonic spinons presents an efficient way to describe them.
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- 2015
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11. Computer programs
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Chris Hamer, Weihong Zheng, and Jaan Oitmaa
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Theoretical computer science ,Lattice (order) ,Graph generator ,Statistical physics ,Series expansion ,Mathematics - Published
- 2006
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12. Series-expansion studies of thet−Jtwo-leg ladder
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Zheng Weihong, Jaan Oitmaa, and Chris Hamer
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Physics ,Condensed matter physics ,Antisymmetric relation ,Bound state ,Condensed Matter::Strongly Correlated Electrons ,Strongly correlated material ,Antibonding molecular orbital ,Dispersion (water waves) ,Series expansion ,Line (formation) ,Phase diagram - Abstract
Series expansions at $T=0$ are used to study properties of the half-filled $t\ensuremath{-}J$ ladder doped with one or two holes, and at quarter filling. Dispersion curves are obtained for one-hole symmetric and antisymmetric (bonding and antibonding) excitations and for the two-hole bound state. The line in the phase diagram that separates bound and unbound states is determined. For quarter filling we compute the ground-state energy and estimate the location of the phase separation line. Comparisons with other numerical and analytical results are presented.
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- 1999
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13. Series expansions for a Heisenberg antiferromagnetic model forSrCu2(BO3)2
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Zheng Weihong, Chris Hamer, and Jaan Oitmaa
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Quantum phase transition ,Physics ,Gapless playback ,Series (mathematics) ,Condensed matter physics ,Phase (matter) ,Spin model ,Zero (complex analysis) ,Antiferromagnetism ,Condensed Matter::Strongly Correlated Electrons ,Series expansion - Abstract
We use a variety of series expansion methods at both zero and finite temperature to study an antiferromagnetic Heisenberg spin model proposed recently by Miyahara and Ueda for the quasi two-dimensional material SrCu$_2$(BO$_3$)$_2$. We confirm that this model exhibits a first-order quantum phase transition at T=0 between a gapped dimer phase and a gapless N\'eel phase when the ratio $x=J'/J$ of nearest and next-nearest neighbour interactions is varied, and locate the transition at $x_c=0.691(6)$. Using longer series we are able to give more accurate estimates of the model parameters by fitting to the high temperature susceptibility data.
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- 1999
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14. Dimer order with striped correlations in theJ1−J2Heisenberg model
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Zheng Weihong, Chris Hamer, Rajiv R. P. Singh, and Jaan Oitmaa
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Physics ,Condensed matter physics ,Heisenberg model ,02 engineering and technology ,021001 nanoscience & nanotechnology ,01 natural sciences ,Resonance (particle physics) ,0103 physical sciences ,Condensed Matter::Strongly Correlated Electrons ,Ising model ,Singlet state ,010306 general physics ,0210 nano-technology ,Series expansion ,Ground state ,Spin (physics) ,Quantum - Abstract
Ground state energies for plaquette and dimer order in the $J_1-J_2$ square-lattice spin-half Heisenberg model are compared using series expansion methods. We find that these energies are remarkably close to each other at intermediate values of $J_2/J_1$, where the model is believed to have a quantum disordered ground state. They join smoothly with those obtained from the Ising expansions for the 2-sublattice N\'eel-state at $J_2/J_1 \approx 0.4$, suggesting a second order transition from a N\'eel state to a quantum disordered state, whereas they cross the energy for the 4-sublattice ordered state at $J_2/J_1 \approx 0.6$ at a large angle, implying a first order transition to the 4-sublattice magnetic state. The strongest evidence that the plaquette phase is not realized in this model comes from the analysis of the series for the singlet and triplet excitation spectra, which suggest an instability in the plaquette phase. Thus, our study supports the recent work of Kotov et al, which presents a strong picture for columnar dimer order in this model. We also discuss the striped nature of spin correlations in this phase, with substantial resonance all along columns of dimers.
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- 1999
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15. Excitation spectrum and ground-state properties of theS=12Heisenberg ladder with staggered dimerization
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Jaan Oitmaa, Valeri N. Kotov, and Zheng Weihong
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Condensed Matter::Quantum Gases ,Physics ,Condensed matter physics ,Bose gas ,Dimer ,Molecular physics ,chemistry.chemical_compound ,chemistry ,Critical line ,Spin wave ,Condensed Matter::Strongly Correlated Electrons ,Spin (physics) ,Ground state ,Series expansion ,Excitation - Abstract
We have studied the excitation spectrum of the $S=1/2$ quantum spin ladder with staggered dimerization by dimer series expansions, diagrammatic analysis of an effective interacting Bose gas of local triplets, and exact diagonalization of small clusters. We find that the model has two massive phases, with predominant inter-chain (rung) or intra-chain correlations. The transition from the rung dimer into the intra-chain dimer phase is characterized by softening of the triplet spectrum at $k=\pi$. The excitation spectrum as well as the spin correlations away from and close to the critical line are calculated. The location of the phase boundary is also determined.
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- 1999
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16. One- and two-hole states in the two-dimensionalt−Jmodel via series expansions
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Jaan Oitmaa, Chris Hamer, and Zheng Weihong
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Physics ,Quantum mechanics ,Dispersion relation ,Binding energy ,P wave ,t-J model ,Bound state ,Strongly correlated material ,Series expansion ,Square lattice - Abstract
We study one- and two-hole properties of the t-J model at half-filling on the square lattice using series expansion methods at T50. The dispersion curve for one-hole excitations is calculated and found to be qualitatively similar to that obtained by other methods, but the bandwidth for small t/J is some 20% larger than given previously. We also obtain the binding energy and dispersion relation for two-hole bound states. The lowest bound state as t/J increases is found to be firstd wave, and then p wave, in accordance with predictions based upon the Kohn-Luttinger effect. We also carry out a similar study for the t-Jz model. @S0163-1829~98!00647-X#
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- 1998
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17. Two-chain spin ladder with frustrating second-neighbor interactions
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Zheng Weihong, Jaan Oitmaa, and Valeri N. Kotov
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Bosonization ,Physics ,Heisenberg model ,Quantum mechanics ,Dispersion relation ,Condensed Matter::Strongly Correlated Electrons ,Ising model ,Abelian group ,Series expansion ,Phase diagram ,Spin-½ - Abstract
The Heisenberg model on a 2-chain spin-1/2 ladder with frustrating second neighbor interactions is studied by using series expansions about the Ising and dimer limits, numerical diagonalization, and by Abelian bosonization analysis. The phase diagram is determined, and pair correlations and the complete dispersion relations for the triplet spin-wave excitations are also computed.
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- 1998
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18. Series expansions for three-dimensional QED
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Zheng Weihong, Jaan Oitmaa, and Chris Hamer
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Physics ,Nuclear and High Energy Physics ,High Energy Physics::Lattice ,High Energy Physics - Lattice (hep-lat) ,Lattice field theory ,FOS: Physical sciences ,Lattice QCD ,Fermion ,Positronium ,symbols.namesake ,High Energy Physics - Lattice ,Hamiltonian lattice gauge theory ,Lattice gauge theory ,Quantum electrodynamics ,symbols ,Hamiltonian (quantum mechanics) ,Series expansion - Abstract
Strong-coupling series expansions are calculated for the Hamiltonian version of compact lattice electrodynamics in (2+1) dimensions, with 4-component fermions. Series are calculated for the ground-state energy per site, the chiral condensate, and the masses of `glueball' and positronium states. Comparisons are made with results obtained by other techniques., Comment: 13 figures
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- 1998
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19. Some graph theory ideas
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Chris Hamer, Jaan Oitmaa, and Weihong Zheng
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Discrete mathematics ,Lattice constant ,Lattice (order) ,Lattice field theory ,Graph theory ,Statistical physics ,Series expansion ,Lattice model (physics) ,Mathematics ,Symmetry number - Published
- 2006
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20. Field dependence of the magnetization for the spin-ladder materialCu2(C5H12N2)2Cl4
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Rajiv R. P. Singh, Jaan Oitmaa, and Zheng Weihong
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Physics ,Condensed matter physics ,Field (physics) ,Isotropy ,Extrapolation ,02 engineering and technology ,021001 nanoscience & nanotechnology ,01 natural sciences ,Magnetization ,0103 physical sciences ,Ising model ,Perturbation theory ,010306 general physics ,0210 nano-technology ,Series expansion ,Anisotropy - Abstract
We have developed a series expansion method for calculating the uniform magnetization, M, as a function of the applied field h for Heisenberg systems at T=0. The method involves introducing Ising anisotropy along the z-axis together with an applied uniform field along the x-axis. On extrapolation to the isotropic limit, one recovers the magnetization for the Heisenberg system with an applied field along the x-axis. This method circumvents the difficulties in developing perturbation theory associated with the commuting nature of the uniform field. The results developed for two-chain ladders appropriate for the material Cu_2(C_5H_{12}N_2)_2Cl_4 are in good agreement with the experimental data. In addition, uniform susceptibility is calculated by high temperature expansions and also compared with the experimental data.
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- 1997
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21. Phase transition and thermal order-by-disorder in the pyrochlore antiferromagnet Er2Ti2O7: A high-temperature series expansion study
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Alexandre G. R. Day, Jaan Oitmaa, Michel J. P. Gingras, Rajiv R. P. Singh, Behnaz Bagheri, and Behnam Javanparast
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Physics ,Phase transition ,Condensed matter physics ,Pyrochlore ,engineering.material ,Condensed Matter Physics ,01 natural sciences ,7. Clean energy ,Spectral line ,Inelastic neutron scattering ,010305 fluids & plasmas ,Electronic, Optical and Magnetic Materials ,Paramagnetism ,Spin wave ,0103 physical sciences ,engineering ,Antiferromagnetism ,Condensed Matter::Strongly Correlated Electrons ,010306 general physics ,Series expansion - Abstract
We use a high-temperature series expansion method to study the phenomenon of thermal order-by-disorder in the rare-earth pyrochlore material Er${}_{2}$Ti${}_{2}$O${}_{7}$ on its approach to the critical temperature ${T}_{c}$. We show that its anisotropic exchange parameters, ${{J}_{e}}$, characterizing an effective spin-1/2 model and recently determined from high-field inelastic neutron scattering spectra, describe very well the thermodynamic properties of the material in the paramagnetic phase and near ${T}_{c}$. While different $\mathbit{q}=0$ $XY$ order-parameter susceptibilities show a high degree of degeneracy, a nonlinear susceptibility, related to the sixth power of the order parameter, reveals a thermal order-by-disorder selection of the same noncollinear ``${\ensuremath{\psi}}_{2}$ state'' as found in Er${}_{2}$Ti${}_{2}$O${}_{7}$. Our results provide a rather definite quantitative demonstration that thermal order-by-disorder is operating at ${T}_{c}$ in this frustrated quantum spin-1/2 antiferromagnetic material.
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- 2013
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22. Exact solution and high-temperature series expansion study of the one-fifth-depleted square-lattice Ising model
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Trinanjan Datta, Jaan Oitmaa, and Simeon Hanks
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Exact solutions in general relativity ,Amplitude ,Ferromagnetism ,Condensed matter physics ,Quartic function ,Square-lattice Ising model ,Ising model ,Coupling (probability) ,Series expansion ,Mathematics - Abstract
The critical behavior of the one-fifth-depleted square-lattice Ising model with nearest-neighbor ferromagnetic interaction has been investigated by means of both an exact solution and a high-temperature series expansion study of the zero-field susceptibility. For the exact solution we employ a decoration transformation followed by a mapping to a staggered eight-vertex model. This yields a quartic equation for the critical coupling giving ${K}_{c}(\ensuremath{\equiv}\ensuremath{\beta}{J}_{c})=0.695$. The series expansion for the susceptibility, to $\mathcal{O}({K}^{18})$, when analyzed via standard Pad\'e approximant methods gives an estimate of ${K}_{c}$, consistent with the exact solution result to at least four significant figures. The series expansion is also analyzed for the leading amplitude and subdominant terms.
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- 2013
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23. S=1bilinear biquadratic spin model on the square lattice: A series expansion study
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Chris Hamer and Jaan Oitmaa
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Physics ,Hamiltonian mechanics ,Bilinear interpolation ,Condensed Matter Physics ,Square lattice ,Electronic, Optical and Magnetic Materials ,symbols.namesake ,Spin model ,symbols ,Antiferromagnetism ,Condensed Matter::Strongly Correlated Electrons ,Hamiltonian (quantum mechanics) ,Series expansion ,Phase diagram ,Mathematical physics - Abstract
We use extensive series expansions at $T=0$ to investigate the phase diagram of a spin-1 Hamiltonian on the square lattice. The model includes bilinear and biquadratic interactions (the ``$J$-$K$'' model) and has been studied recently using a variety of other methods. We find a clear indication of the three-sublattice order conjectured recently by Toth et al. [Phys. Rev. B 85, 140403(R) (2012)]. We also compute the energy and order parameter in the quadrupolar phases.
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- 2013
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24. Disorder Line and Incommensurate Floating Phases in the Quantum Ising Model on an Anisotropic Triangular Lattice
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Richard T. Scalettar, Jaan Oitmaa, Vladimir Iglovikov, and Rajiv R. P. Singh
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Physics ,Phase transition ,Condensed matter physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Quantum Monte Carlo ,Exchange interaction ,FOS: Physical sciences ,Condensed Matter Physics ,01 natural sciences ,Square lattice ,010305 fluids & plasmas ,Electronic, Optical and Magnetic Materials ,Condensed Matter - Strongly Correlated Electrons ,Quantum Gases (cond-mat.quant-gas) ,Quantum mechanics ,0103 physical sciences ,Antiferromagnetism ,Hexagonal lattice ,Ising model ,010306 general physics ,Series expansion ,Condensed Matter - Quantum Gases - Abstract
We present a Quantum Monte Carlo study of the Ising model in a transverse field on a square lattice with nearest-neighbor antiferromagnetic exchange interaction J and one diagonal second-neighbor interaction $J'$, interpolating between square-lattice ($J'=0$) and triangular-lattice ($J'=J$) limits. At a transverse-field of $B_x=J$, the disorder-line first introduced by Stephenson, where the correlations go from Neel to incommensurate, meets the zero temperature axis at $J'\approx 0.7 J$. Strong evidence is provided that the incommensurate phase at larger $J'$, at finite temperatures, is a floating phase with power-law decaying correlations. We sketch a general phase-diagram for such a system and discuss how our work connects with the previous Quantum Monte Carlo work by Isakov and Moessner for the isotropic triangular lattice ($J'=J$). For the isotropic triangular-lattice, we also obtain the entropy function and constant entropy contours using a mix of Quantum Monte Carlo, high-temperature series expansions and high-field expansion methods and show that phase transitions in the model in presence of a transverse field occur at very low entropy.
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- 2013
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25. Convergent Expansions for Properties of the Heisenberg Model forCaV4O9
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Jaan Oitmaa, Zheng Weihong, Chris Hamer, Rajiv R. P. Singh, and Martin P. Gelfand
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Physics ,Condensed matter physics ,Heisenberg model ,Computer Science::Information Retrieval ,General Physics and Astronomy ,Magnetic susceptibility ,symbols.namesake ,symbols ,Antiferromagnetism ,Condensed Matter::Strongly Correlated Electrons ,Neutron ,Perturbation theory ,Series expansion ,Excitation ,Raman scattering - Abstract
We have constructed high-order {ital T}=0 expansions for the elementary excitation spectra, and high-temperature expansions for the susceptibility, for the {ital S}=1/2 Heisenberg antiferromagnet believed to describe the spin-gap system CaV{sub 4}O{sub 9}. Existing susceptibility data are analyzed using these theoretical results. If nearest- and second-neighbor interactions are in the ratio 2:1, there should be clear indications in both neutron and Raman scattering. {copyright} {ital 1996 The American Physical Society.}
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- 1996
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26. Series expansion for theJ1-J2Heisenberg antiferromagnet on a square lattice
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Jaan Oitmaa and Zheng Weihong
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Physics ,Statistics::Theory ,Magnetization ,Statistics::Applications ,Condensed matter physics ,Antiferromagnetism ,Order (ring theory) ,Condensed Matter::Strongly Correlated Electrons ,Ising model ,Ground state ,Series expansion ,Square lattice ,Phase diagram - Abstract
We have developed series expansions about the Ising limit for the ground state energy, magnetization, susceptibility, and energy gap of the frustrated ${\mathit{J}}_{1}$-${\mathit{J}}_{2}$ antiferromagnet. We find that the N\'eel order vanishes at ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$\ensuremath{\simeq}0.4 and collinear order sets in around ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$\ensuremath{\simeq}0.6, in broad agreement with other recent work. We also explore the nature of the phase diagram for the spin-anisotropic case. \textcopyright{} 1996 The American Physical Society.
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- 1996
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27. Quantum spin ladders atT=0 and at high temperatures studied by series expansions
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Jaan Oitmaa, Rajiv R. P. Singh, and Weihong Zheng
- Subjects
Physics ,Condensed matter physics ,01 natural sciences ,Magnetic susceptibility ,Power law ,010305 fluids & plasmas ,Correlation function (statistical mechanics) ,Ferromagnetism ,Dispersion relation ,0103 physical sciences ,Antiferromagnetism ,Condensed Matter::Strongly Correlated Electrons ,010306 general physics ,Series expansion ,Spin (physics) - Abstract
We have carried out extensive series studies, at T50 and at high temperatures, of two-chain and three-chain spin-half ladder systems with antiferromagnetic intrachain and both antiferromagnetic and ferromagnetic interchain couplings. Our results confirm the existence of a gap in the two-chain Heisenberg ladders for all nonzero values of the interchain couplings. Complete dispersion relations for the spin-wave excitations are computed. For three-chain systems, our results are consistent with a gapless spectrum. We also calculate the uniform magnetic susceptibility and specific heat as a function of temperature. We find that asT!0, for the two-chain system the uniform susceptibility goes rapidly to zero, whereas for the three-chain system it approaches a finite value. These results are compared in detail with previous studies of finite systems.@S01631829~96!06226-1# The magnetic properties of low dimensional systems have been the subject of intense theoretical and experimental research in recent years. It is by now well established that one-dimensional Heisenberg antiferromagnets with integer spin have a gap in the excitation spectrum, whereas those with half-integer spin have gapless excitations. The former have a finite correlation length, while for the latter it is infinite with the spin-spin correlation function decaying to zero as a power law. In two dimensions, the unfrustrated square
- Published
- 1996
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28. Comparison between linked-cluster expansion methods for the U(1) lattice gauge model in 2+1 dimensions
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Zheng Weihong, Chris Hamer, and Jaan Oitmaa
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Physics ,Nuclear and High Energy Physics ,Lattice field theory ,Geometry ,Atomic and Molecular Physics, and Optics ,symbols.namesake ,Hamiltonian lattice gauge theory ,Quantum electrodynamics ,Lattice (order) ,symbols ,U-1 ,Hamiltonian (quantum mechanics) ,Series expansion ,Mathematics ,Mathematical physics ,Cluster expansion - Abstract
Comparisons are made between two different linked-cluster expansion methods, namely, the t expansion and the strong-coupling series expansion, as applied to the compact U(1) lattice gauge model in 2+1 dimensions. Connected moments of the Hamiltonian are calculated up to 28th order, extending previous results of Morningstar, and are used to form a t expansion. The t expansion is technically easier to calculate, and can give estimates of the axial string tension, which the strong-coupling series expansion cannot; but the strong-coupling series expansion gives better results for the mass gaps. \textcopyright{} 1996 The American Physical Society.
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- 1996
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29. High-temperature series expansion study of the Heisenberg antiferromagnet on the hyperkagome lattice: Comparison with Na4Ir3O8
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Rajiv R. P. Singh and Jaan Oitmaa
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Physics ,Condensed matter physics ,Heisenberg model ,02 engineering and technology ,Approx ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,01 natural sciences ,Magnetic susceptibility ,Heat capacity ,Electronic, Optical and Magnetic Materials ,0103 physical sciences ,Antiferromagnetism ,Quantum spin liquid ,010306 general physics ,0210 nano-technology ,Series expansion ,Structure factor - Abstract
We develop high-temperature series expansions for ln $\mathrm{Z}$ and the uniform structure factor of the spin-half Heisenberg model on the hyperkagome lattice to the order of ${\ensuremath{\beta}}^{16}$. These expansions are used to calculate the uniform susceptibility ($\ensuremath{\chi}$), the entropy ($S$), and the heat capacity ($C$) of the model as a function of temperature. Series extrapolations of the expansions converge well down to a temperature of approximately $J/4$. A comparison with the experimental data for Na${}_{4}$Ir${}_{3}$O${}_{8}$ shows that its magnetic susceptibility is reasonably well described by the model with an exchange constant $J\ensuremath{\approx}300$ K, but there are also additional smaller terms present in the system. The specific heat of the model has two peaks. The lower-temperature peak, which is just below our range of convergence, contains about 40$%$ of the total entropy. Despite being a three-dimensional lattice, this model shares many features with the kagome-lattice Heisenberg model and the material must be considered a strong candidate for a quantum spin liquid.
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- 2012
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30. Restoration of symmetry in the spectrum of the bilayer Heisenberg antiferromagnet
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Zheng Weihong, Chris Hamer, and Jaan Oitmaa
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Quantum phase transition ,Physics ,Condensed matter physics ,Critical point (thermodynamics) ,Heisenberg model ,Magnon ,Degenerate energy levels ,Condensed Matter::Strongly Correlated Electrons ,Condensed Matter Physics ,Series expansion ,Square lattice ,Multiplet ,Electronic, Optical and Magnetic Materials - Abstract
The longitudinal mode in the Heisenberg model on a bilayer square lattice is studied using series expansion methods. It is demonstrated numerically that the longitudinal mode becomes degenerate with the magnon modes at the quantum phase transition between N\'eel and dimerized phases, thus forming a spin-1 multiplet, in accord with the restoration of SU(2) symmetry. Finally, it is shown that the magnon mode becomes degenerate with the triplet mode in the dimerized phase at the critical point, showing continuity of the excitation spectrum across the critical point.
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- 2012
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31. Series expansions for the 3D transverse Ising model at T=0
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Jaan Oitmaa, Zheng Weihong, and Chris Hamer
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Magnetization ,Condensed matter physics ,Transverse ising model ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Square-lattice Ising model ,Ising model ,Renormalization group ,Cubic crystal system ,Series expansion ,Mathematical Physics ,Mathematics ,Universality (dynamical systems) - Abstract
Both weak-coupling and strong-coupling series expansions are calculated for the Ising model in a transverse field at zero temperature in three dimensions. Series are obtained for the ground-state energy, the magnetization, the susceptibility, and the energy gaps, on the simple cubic, the body-centred cubic and the face-centred cubic lattices. The analysis of the critical behaviour is consistent with the behaviour predicted by renormalization group theory for the four-dimensional simple Ising model. There is a remarkable degree of universality between all three lattices.
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- 1994
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32. Phase diagram of theJ1−J2−J3Heisenberg model on the honeycomb lattice: A series expansion study
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Jaan Oitmaa and Rajiv R. P. Singh
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Power series ,Physics ,Condensed matter physics ,Heisenberg model ,02 engineering and technology ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,01 natural sciences ,Electronic, Optical and Magnetic Materials ,Magnetization ,Spin wave ,Lattice (order) ,0103 physical sciences ,Ising model ,010306 general physics ,0210 nano-technology ,Series expansion ,Phase diagram - Abstract
We study magnetically-ordered phases and their phase boundaries in the ${J}_{1}\ensuremath{-}{J}_{2}\ensuremath{-}{J}_{3}$ Heisenberg models on the honeycomb lattice using series expansions around N\'eel and different colinear and noncolinear magnetic states. An Ising anisotropy ($\ensuremath{\lambda}={J}_{\ensuremath{\perp}}/{J}_{z}\ensuremath{\ne}1$) is introduced and ground-state energy and magnetization order parameter are calculated as a power series expansion in $\ensuremath{\lambda}$. Series extrapolation methods are used to study properties for the Heisenberg model ($\ensuremath{\lambda}=1$). We find that at large ${J}_{3}$ ($g0.6$) there is a first-order transition between N\'eel and columnar states, in agreement with the classical answer. For ${J}_{3}=0$, we find that the N\'eel phase extends beyond the region of classical stability. We also find that spiral phases are stabilized over large parameter regions, although their spiral angles can be substantially renormalized with respect to the classical values. Our study also shows a magnetically disordered region at intermediate ${J}_{2}/{J}_{1}$ and ${J}_{3}/{J}_{1}$ values.
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- 2011
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33. Corrections to Pauling residual entropy and single tetrahedron based approximations for the pyrochlore lattice Ising antiferromagnet
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Jaan Oitmaa and Rajiv R. P. Singh
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Physics ,Condensed matter physics ,Statistical Mechanics (cond-mat.stat-mech) ,FOS: Physical sciences ,Approx ,Condensed Matter Physics ,01 natural sciences ,Pyrochlore lattice ,3. Good health ,010305 fluids & plasmas ,Electronic, Optical and Magnetic Materials ,Spin wave ,0103 physical sciences ,Tetrahedron ,Antiferromagnetism ,Ising model ,010306 general physics ,Series expansion ,Residual entropy ,Condensed Matter - Statistical Mechanics - Abstract
We study corrections to single tetrahedron based approximations for the entropy, specific heat and uniform susceptibility of the pyrochlore lattice Ising antiferromagnet, by a Numerical Linked Cluster (NLC) expansion. In a tetrahedron based NLC, the first order gives the Pauling residual entropy of ${1\over 2}\log{3\over 2}\approx 0.20273$. A 16-th order NLC calculation changes the residual entropy to 0.205507 a correction of 1.37 percent over the Pauling value. At high temperatures, the accuracy of the calculations is verified by a high temperature series expansion. We find the corrections to the single tetrahedron approximations to be at most a few percent for all the thermodynamic properties., Comment: 5 pages, 5 figures. Version as published in PRB
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- 2011
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34. Large-Uexpansions for the Hubbard model atT=0. II
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Zheng Weihong, Yang Jie, J.A. Henderson, and Jaan Oitmaa
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Physics ,Electron density ,Distribution (mathematics) ,Series (mathematics) ,Hubbard model ,Computer Science::Information Retrieval ,Padé approximant ,Perturbation theory ,Series expansion ,Ground state ,Mathematical physics - Abstract
We investigate the ground state of the Hubbard model in one and two dimensions. Long perturbation expansions in [ital t]/[ital U], i.e., about the atomic limit, are computed for the ground-state energy of finite lattices with [ital N][le]10 for arbitrary electron density. We also extend the series for the one-dimensional infinite lattice by expanding the Bethe-ansatz equations. Pade-approximant analysis of the series shows a distribution of singularities that varies dramatically with the electron density [ital n]. We also investigate the effect of inclusion of next-nearest-neighbor hopping. This appears to have little effect at half-filling but is significant away from half-filling.
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- 1993
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35. Two-parameter expansions for quantum spin systems
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Zheng Weihong and Jaan Oitmaa
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Physics ,Condensed matter physics ,Heisenberg model ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Square lattice ,Magnetic field ,Quantum mechanics ,Quantum system ,Condensed Matter::Strongly Correlated Electrons ,Ising model ,Perturbation theory (quantum mechanics) ,Series expansion ,Mathematical Physics ,Lattice model (physics) - Abstract
As an extension of a one-parameter series expansion, a two-parameter expansion technique for quantum spin systems is developed. As examples of the method the authors present results for three different models on the square lattice: the (2+1)-dimensional Ising model with an external magnetic field, and the Heisenberg antiferromagnet with both an external staggered parallel magnetic field and an external perpendicular magnetic field. Analysis of the resulting series is also presented.
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- 1992
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36. Quantum phase diagram and excitations for the one-dimensionalS=1Heisenberg antiferromagnet with single-ion anisotropy
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Jaan Oitmaa, A. Fabricio Albuquerque, and Chris Hamer
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Physics ,Quantum phase transition ,Optical phase space ,Condensed matter physics ,Quantum mechanics ,Quantum Monte Carlo ,Antiferromagnetism ,Condensed Matter Physics ,Anisotropy ,Series expansion ,Quantum ,Electronic, Optical and Magnetic Materials ,Phase diagram - Abstract
We investigate the zero-temperature phase diagram of the one-dimensional S=1 Heisenberg antiferromagnet with single-ion anisotropy. By employing high-order series expansions and quantum Monte Carlo simulations we obtain accurate estimates for the critical points separating different phases in the quantum phase diagram. Additionally, excitation spectra and gaps are obtained.
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- 2009
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37. Low-temperature series expansions for the (2+1)-dimensional Ising model
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Zheng Weihong, Jaan Oitmaa, and Chris Hamer
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General Physics and Astronomy ,Padé approximant ,Statistical and Nonlinear Physics ,Square-lattice Ising model ,Ising model ,Series expansion ,Square lattice ,Mathematical Physics ,Mass gap ,Mathematics ,Cluster expansion ,Universality (dynamical systems) ,Mathematical physics - Abstract
Using efficient cluster expansion methods, the known high-temperature series for the vacuum energy, specific heat, susceptibility and mass gap of the (2+1)-dimensional Ising model on the square and triangular lattices have been extended by several terms. Estimates of the critical indices demonstrate very convincing universality with the Euclidean version of the model.
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- 1991
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38. Square-lattice Heisenberg antiferromagnet atT=0
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Jaan Oitmaa, Chris Hamer, and Zheng Weihong
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Physics ,Condensed matter physics ,Series (mathematics) ,Heisenberg model ,High Energy Physics::Lattice ,Quantum mechanics ,Antiferromagnetism ,Condensed Matter::Strongly Correlated Electrons ,Ising model ,Series expansion ,Square lattice ,Absolute zero ,Mass gap - Abstract
The spin-1/2 and spin-1 Heisenberg antiferromagnets on a square lattice are studied via series expansions around the Ising limit. Series are calculated for the ground-state energy, staggered magnetization, transverse susceptibility, staggered parallel susceptibility, and mass gap. Extrapolating these series to the isotropic limit, we find extremely good agreement with the predictions of spin-wave theory.
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- 1991
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39. Discerning incompressible and compressible phases of cold atoms in optical lattices
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Lode Pollet, Matthias Troyer, Vito Scarola, and Jaan Oitmaa
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Condensed Matter::Quantum Gases ,Physics ,Quantum Physics ,Condensed matter physics ,FOS: Physical sciences ,General Physics and Astronomy ,Edge (geometry) ,Condensed Matter - Other Condensed Matter ,Core (optical fiber) ,Phase (matter) ,Compressibility ,Quantum Physics (quant-ph) ,Series expansion ,Other Condensed Matter (cond-mat.other) - Abstract
Experiments with cold atoms trapped in optical lattices offer the potential to realize a variety of novel phases but suffer from severe spatial inhomogeneity that can obscure signatures of new phases of matter and phase boundaries. We use a high temperature series expansion to show that compressibility in the core of a trapped Fermi-Hubbard system is related to measurements of changes in double occupancy. This core compressibility filters out edge effects, offering a direct probe of compressibility independent of inhomogeneity. A comparison with experiments is made.
- Published
- 2008
40. Studies of lattice spin systems using series expansions
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Chris Hamer, Jaan Oitmaa, and Weihong Zheng
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Physics ,symbols.namesake ,Reciprocal lattice ,Condensed matter physics ,Heisenberg model ,symbols ,Condensed Matter::Strongly Correlated Electrons ,Ising model ,Ground state ,Hamiltonian (quantum mechanics) ,Series expansion ,Lattice model (physics) ,Cluster expansion - Abstract
Efficient cluster expansion techniques have been developed for quantum Hamiltonian lattice models. Applications to antiferromagnetic Heisenberg systems, based on expansion about the Ising limit, yield accurate results for both ground state properties and excitation spectra. Recent work on novel systems, including spin ladders and frustrated two-dimensional systems, will be described.
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- 2008
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41. Application of linked-cluster expansions to quantum hamiltonian lattice systems
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Chris Hamer, Jaan Oitmaa, and Weihong Zheng
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Square lattice ,symbols.namesake ,Lanczos resampling ,Coupled cluster ,Lattice (order) ,Lattice gauge theory ,Quantum electrodynamics ,symbols ,Condensed Matter::Strongly Correlated Electrons ,Ground state ,Hamiltonian (quantum mechanics) ,Series expansion ,Mathematics ,Mathematical physics - Abstract
Comparisons are made between several different linked-cluster expansion methods, namely the linked-cluster perturbation series expansion, the t-expansion, the analytic Lanczos expansion, and the coupled-cluster expansion. They are considered from a technical point of view, and also as applied to the S=1/2 Heisenberg antiferromagnet on the square lattice and the compact U(1) lattice gauge model in 2+1 dimensions.
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- 2008
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42. One-particle dispersion and spectral weights in the transverse Ising model
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Weihong Zheng, Chris Hamer, and Jaan Oitmaa
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Physics ,Series (mathematics) ,Spin wave ,Quantum mechanics ,Square-lattice Ising model ,Statistical physics ,Condensed Matter Physics ,Quantum statistical mechanics ,Structure factor ,Series expansion ,Critical exponent ,Square (algebra) ,Electronic, Optical and Magnetic Materials - Abstract
The one-particle contribution to the dynamical structure factor is explored for the simple case of the transverse Ising model, using series expansion methods. The critical behavior of the spectral weight is found to conform with the general predictions of Sachdev. For the linear chain, exact results are obtained, and confirmed by correspondence with exactly known results for the correlation functions of the quantum $XY$ model in one dimension. In higher dimensions, series are calculated for the triangular, square, and simple cubic lattices, and numerical estimates for the critical exponents are found to agree with expectations, within errors.
- Published
- 2006
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43. Hard-core bosons on the triangular lattice at zero temperature: A series expansion study
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Jaan Oitmaa, D. Tompsett, and Weihong Zheng
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Quantum phase transition ,Physics ,Series (mathematics) ,Condensed matter physics ,FOS: Physical sciences ,Condensed Matter Physics ,Electronic, Optical and Magnetic Materials ,Condensed Matter - Other Condensed Matter ,Superfluidity ,Quantum mechanics ,Quantum critical point ,Phase (matter) ,Hexagonal lattice ,Series expansion ,Other Condensed Matter (cond-mat.other) ,Boson - Abstract
We use high order linked cluster series to investigate the hard core boson model on the triangular lattice, at zero temperature. Our expansions, in powers of the hopping parameter $t$, probe the spatially ordered `solid' phase and the transition to a uniform superfluid phase. At the commensurate fillings $n=1/3, 2/3$ we locate a quantum phase transition point at $(t/V)_c\simeq 0.208(1)$, in good agreement with recent Monte Carlo studies. At half-filling ($n=1/2$) we find evidence for a solid phase, which persists to $t/V\simeq 0.06$., 13 pages, 7 figures
- Published
- 2006
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44. Quantum spin models at T = 0
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Chris Hamer, Jaan Oitmaa, and Weihong Zheng
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Condensed matter physics ,Quantum mechanics ,Lattice (order) ,Quasiparticle ,Ising model ,Quantum spin liquid ,Series expansion ,Ground state ,Lattice model (physics) ,Quantum dimer models ,Mathematics - Published
- 2006
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45. Additional topics
- Author
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Weihong Zheng, Jaan Oitmaa, and Chris Hamer
- Subjects
Physics ,Random field ,Lattice (order) ,Quantum mechanics ,Ising model ,Statistical physics ,Series expansion - Published
- 2006
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46. Series expansions for lattice gauge models
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Jaan Oitmaa, Chris Hamer, and Weihong Zheng
- Subjects
Physics ,Hamiltonian lattice gauge theory ,Quantum mechanics ,Lattice gauge theory ,Lattice (order) ,Lattice field theory ,Lattice QCD ,Series expansion ,Asymptotic freedom ,Lattice model (physics) ,Mathematical physics - Published
- 2006
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47. Introduction
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Jaan Oitmaa, Weihong Zheng, and Chris Hamer
- Subjects
Physics ,Hubbard model ,Lattice gauge theory ,Quantum mechanics ,Thermodynamic limit ,Ising model ,Strongly correlated material ,Statistical physics ,Series expansion ,Classical XY model ,Analytic function - Published
- 2006
- Full Text
- View/download PDF
48. Models with continuous symmetry and the free graph expansion
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Jaan Oitmaa, Weihong Zheng, and Chris Hamer
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Renormalization ,Phase transition ,Singularity ,Lattice constant ,Continuous symmetry ,Quantum electrodynamics ,Lattice (order) ,Statistical physics ,Curvature ,Series expansion ,Mathematics - Published
- 2006
- Full Text
- View/download PDF
49. Critical Behaviour of One-particle Spectral Weights in the Transverse Ising Model
- Author
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Zheng Weihong, Jaan Oitmaa, Ross H. McKenzie, and Chris Hamer
- Subjects
Quantum phase transition ,Physics ,Series (mathematics) ,Strongly Correlated Electrons (cond-mat.str-el) ,FOS: Physical sciences ,Condensed Matter Physics ,Square lattice ,Square (algebra) ,Electronic, Optical and Magnetic Materials ,Condensed Matter - Strongly Correlated Electrons ,Spin wave ,Statistical physics ,Series expansion ,Quantum statistical mechanics ,Critical exponent - Abstract
We investigate the critical behaviour of the spectral weight of a single quasiparticle, one of the key observables in experiment, for the particular case of the transverse Ising model.Series expansions are calculated for the linear chain and the square and simple cubic lattices. For the chain model, a conjectured exact result is discovered. For the square and simple cubic lattices, series analyses are used to estimate the critical exponents. The results agree with the general predictions of Sachdev., Comment: 4 pages, 3 figures
- Published
- 2006
- Full Text
- View/download PDF
50. Thermodynamics of a spin-12chain coupled to Einstein phonons
- Author
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Götz S. Uhrig, Jaan Oitmaa, and Alexander Bühler
- Subjects
Physics ,Phonon ,Degrees of freedom (physics and chemistry) ,Thermodynamics ,Statistical mechanics ,Condensed Matter Physics ,Electronic, Optical and Magnetic Materials ,Coupling (physics) ,symbols.namesake ,symbols ,Einstein ,Series expansion ,Adiabatic process ,Spin-½ - Abstract
A high order series expansion is employed to study the thermodynamical properties of a S=1/2 chain coupled to dispersionless phonons. The results are obtained without truncating the phonon subspace since the series expansion is performed formally in the overall exchange coupling J. The results are used to investigate various parameter regimes, e.g. the adiabatic and antiadiabatic limit as well as the intermediate regime which is difficult to investigate by other methods. We find that dynamic phonon effects become manifest when more than one thermodynamic quantity is analyzed.
- Published
- 2004
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- View/download PDF
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