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We use finite temperature strong coupling expansions to calculate thermodynamic properties of the Honeycomb-lattice SU(4) Hubbard model. We present numerical results for various properties including chemical potential, compressibility, entropy and specific heat as a function of temperature and density at several $U/t$ values. We study the onset of charge incompressibility and Mott gaps as the temperature is lowered at integer densities. In the incompressible Mott regime, the expansions are recast into a high temperature expansion for a generalized spin model with SU(4) symmetry, which is then used to study the convergence of strong coupling expansions in t/U. We discuss lessons that can be drawn from high temperature properties of a simple Hubbard model regarding Twisted Bilayer Graphene (TBG) and other magic-angle flat-band systems., 6 pages, 6 figures

We develop finite temperature strong coupling expansions for the SU(N) Hubbard Model in powers of $\beta t$, $w=\exp{(-\beta U)}$ and ${1\over \beta U}$ for arbitrary filling. The expansions are done in the grand canonical ensemble and are most useful at a density of one particle per site, where for $U$ larger than or of order the Bandwidth, the expansions converge over a wide temperature range $t^2/U \ \lesssim \ T \ \lesssim \ 10 U$. By taking the limit $w\to 0$, valid at temperatures much less than $U$, the expansions turn into a high temperature expansion for a dressed SU(N) Heisenberg model that includes nearest-neighbor exchange, further neighbor exchanges and ring exchanges known from the $T=0$ perturbation theory of the SU(2) Hubbard model. Below a filling of one particle per site, the $w\to 0$ limit corresponds to an effective $t-J$ model. The onset of strong correlations can be identified by a plateau-like behavior in the entropy as a function of temperature. At small deviations from one particle per site, the expansions can be arranged in powers of a small parameter $\delta=1-n$, the deviation from one particle per site, where the leading $\beta t$ dependent terms correspond to holes sloshing around in a disordered SU(N) background. We use these expansions to calculate the thermodynamic properties of the model at moderate and high temperatures over a wide parameter range., Comment: 8 pages 7 figures

We use series expansion methods to investigate the zero-temperature phase diagram of a spin-$\frac{1}{2}$ Heisenberg frustrated bilayer model. For different parameter regions the model shows two related antiferromagnetic phases as well as a nonmagnetic dimerized phase. The phase boundaries are located to high precision and agree very well with a previous calculation using different methods. The triplon spectrum in the dimerized phase is also studied.

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.

We study the thermodynamic properties of modified spin-$S$ Kitaev models introduced by Baskaran, Sen and Shankar (Phys. Rev. B 78, 115116 (2008)). These models have the property that for half-odd-integer spins their eigenstates map on to those of spin-1/2 Kitaev models, with well-known highly entangled quantum spin-liquid states and Majorana fermions. For integer spins, the Hamiltonian is made out of commuting local operators. Thus, the eigenstates can be chosen to be completely unentangled between different sites, though with a significant degeneracy for each eigenstate. For half-odd-integer spins, the thermodynamic properties can be related to the spin-1/2 Kitaev models apart from an additional degeneracy. Hence we focus here on the case of integer spins. We use transfer matrix methods, high temperature expansions and Monte Carlo simulations to study the thermodynamic properties of ferromagnetic and antiferromagnetic models with spin $S=1$ and $S=2$. Apart from large residual entropies, which all the models have, we find that they can have a variety of different behaviors. Transfer matrix calculations show that for the different models, the correlation lengths can be finite as $T\to 0$, become critical as $T\to 0$ or diverge exponentially as $T\to 0$. There is a conserved $Z_2$ flux variable associated with each hexagonal plaquette which saturates at the value $+1$ as $T\rightarrow0$ in all models except the $S=1$ antiferromagnet where the mean flux remains zero as $T\to 0$. We provide qualitative explanations for these results., 14 pages and 7 figures

Antiferromagnetic quantum spin systems can exhibit a transition between collinear and spiral ground states, driven by frustration. Classically this is a smooth crossover and the crossover point is termed a Lifshitz point. Quantum fluctuations change the nature of the transition. In particular, it has been argued previously that in the two-dimensional (2D) case a spin liquid (SL) state is developed in the vicinity of the Lifshitz point, termed a Lifshitz SL. In the present work, using a field theory approach, we solve the Lifshitz quantum phase transition problem for the 2D frustrated XY model. Specifically, we show that, unlike the $SU(2)$ symmetric Lifshitz case, in the XY model, the SL exists only at the critical point. At zero temperature we calculate nonuniversal critical exponents in the N\'eel and in the spin spiral state and relate these to properties of the SL. We also solve the transition problem at a finite temperature and discuss the role of topological excitations.

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.

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.

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

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

The perovskite ${\mathrm{Ba}}_{8}{\mathrm{CoNb}}_{6}{\mathrm{O}}_{24}$ comprises equilateral effective spin-$\frac{1}{2} {\mathrm{Co}}^{2+}$ triangular layers separated by six nonmagnetic layers. Susceptibility, specific heat, and neutron scattering measurements combined with high-temperature series expansions and spin-wave calculations confirm that ${\mathrm{Ba}}_{8}{\mathrm{CoNb}}_{6}{\mathrm{O}}_{24}$ is basically a two-dimensional magnet with no detectable spin anisotropy and no long-range magnetic ordering down to 0.06 K. In other words, ${\mathrm{Ba}}_{8}{\mathrm{CoNb}}_{6}{\mathrm{O}}_{24}$ is very close to be a realization of the paradigmatic spin-$\frac{1}{2}$ triangular Heisenberg model, which is not expected to exhibit symmetry breaking at finite temperatures according to the Mermin and Wagner theorem.

Motivated by the discovery of spiral and modulated collinear phases in several magnetic materials, we investigate the magnetic properties of Heisenberg spin $S=1/2$ antiferromagnets in two and three dimensions, with frustration arising from second-neighbor couplings in one axial direction [the axial next-nearest-neighbor Heisenberg (ANNNH) model]. Our results clearly demonstrate the presence of an incommensurate spiral phase at $T=0$ in two dimensions, extending to finite temperatures in three dimensions. The crossover between N\'eel and spiral order occurs at a value of the frustration parameter considerably above the classical value 0.25, a sign of substantial quantum fluctuations. We also investigate a possible modulated collinear phase with a wavelength of four lattice spacings and find that it has substantially higher energy and hence is not realized in the model.

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

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.

If magnetic frustration is most commonly known for undermining long-range order, as famously illustrated by spin liquids, the ability of matter to develop new collective mechanisms in order to fight frustration is perhaps no less fascinating, providing an avenue for the exploration and discovery of unconventional behaviors. Here, we study a realistic minimal model where a number of such mechanisms converge, which, incidentally, pertain to the perplexing quantum spin ice candidate Yb(2)Ti(2)O(7). Specifically, we explain how thermal and quantum fluctuations, optimized by order-by-disorder selection, conspire to expand the stability region of a degenerate continuous U(1) manifold against the classical splayed ferromagnetic ground state that is displayed by the sister compound Yb(2)Ti(2)O(7). The resulting competition gives rise to multiple phase transitions, in striking similitude with recent experiments on Yb(2)Ti(2)O(7) [Lhotel et al., Phys. Rev. B 89, 224419 (2014)]. By combining a gamut of numerical techniques, we obtain compelling evidence that such multiphase competition is a natural engine for the substantial sample-to-sample variability observed in Yb(2)Ti(2)O(7) and is the missing key to ultimately understand the intrinsic properties of this material. As a corollary, our work offers a pertinent illustration of the influence of chemical pressure in rare-earth pyrochlores.

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.

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.

Exchange couplings are calculated for Li2VOSiO4 using local density approximation (LDA). From a two band tight-binding model fitted to the LDA band structure and mapped to a Heisenberg model, the in-plane and inter-plane exchange integrals are obtained. While the sum of in-plane couplings J1+J2=9.5±1.5 K and the inter-plane coupling J⊥ ~ 0.2-0.3 K agree with recent experimental data, the ratio J2/J1 ~ 12 exceeds the reported value by an order of magnitude. Using geometrical considerations, high temperature expansions and perturbative mean field theory, we show that the LDA derived exchange constants lead to a remarkably accurate description of the properties of these materials including specific heat, susceptibility and Neél temperatures.

We study the nearest-neighbor exchange (${J}_{1}$) and second-nearest-neighbor exchange (${J}_{2}$) $XY$ antiferromagnet on the honeycomb lattice using ground state series expansions around N\'eel, columnar, and dimer phases. The conventional two-sublattice $XY$ N\'eel order at small ${J}_{2}$ vanishes at ${J}_{2}/{J}_{1}=0.22\ifmmode\pm\else\textpm\fi{}0.01$ in agreement with results from density matrix renormalization group (DMRG) studies. Near the transition, we find evidence for an approximate emergent symmetry between $XY$ and Ising degrees of freedom, namely the nearest-neighbor Ising and $XY$ spin correlations become nearly equal. This suggests that the system is close to a bicritical point separating $XY$ and Ising orders. At still larger ${J}_{2}/{J}_{1}$ the columnar and dimer energies are found to be nearly degenerate. At even larger ${J}_{2}$ the columnar phase is obtained. The ground state energies in all three phases are in good agreement with the values found in the DMRG studies.

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.

We analyze the stability of the spontaneously dimerized phase of the frustrated Heisenberg antiferromagnet\char22{}the ${J}_{1}{\ensuremath{-}J}_{2}$ model\char22{}in two dimensions. The lowest triplet excitation, corresponding to breaking of a singlet bond, is found to be stable in the region $0.38\ensuremath{\lesssim}{J}_{2}{/J}_{1}\ensuremath{\lesssim}0.62.$ In addition we find a stable low-energy collective singlet mode, which reflects the spontaneous violation of the discrete symmetry. The spontaneous dimerization vanishes at the point of second-order quantum transition into the N\'eel ordered phase $[{(J}_{2}{/J}_{1}{)}_{c1}\ensuremath{\approx}0.38].$ We argue that the disappearance of dimer order is related to the vanishing of the singlet energy gap at the transition point.

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.

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.

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.

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#

We study antiferromagnetic, $S=1/2$ Heisenberg models with nearest- and second-neighbor interactions on the one-fifth depleted square lattice which describes the spin degrees of freedom in the spin-gap system ${\mathrm{CaV}}_{4}{\mathrm{O}}_{9}.$ The metaplaquette expansion for the triplet excitation spectrum is extended to fifth order, and the results are compared with experimental data on ${\mathrm{CaV}}_{4}{\mathrm{O}}_{9}.$ We attempt to locate the phase boundary between magnetically ordered and gapped phases.

The two-dimensional quantum Heisenberg antiferromagnet at zero temperature, with locally frustrating magnetic defects, is studied. We consider two types of defects---an isolated ferromagnetic bond (FMB) and a quantum impurity spin, coupled symmetrically to the two sublattices. A technique is developed to study strong defect-environment interaction. In the case of a FMB we find that, contrary to the previous linear spin-wave result, the local magnetization stays finite even for strong frustration. For an antiferromagnetic coupling of a quantum impurity spin with its environment, we find a local change in the ground state. All our calculations are compared with numerical results from exact diagonalization.

We analyze the ground state properties of the two-dimensional quantum antiferromagnet with a S=1/2 Kondo impurity. Perturbation theory around the strong Kondo coupling limit is developed and the results compared with studies, based on exact diagonalization of small clusters. We find that at intermediate coupling the impurity is partially screened and the magnetization locally suppressed. A local singlet between the impurity and the host spin is formed asymptotically., Comment: 12 REVTex pages, 4 Postscript figures

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.

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

Description of the presentations and the discussions on quantum spin liquids held at ICM'97.

For anisotropic Heisenberg ferromagnet of S = 1 with the bilinear exchange interaction J and the biquadratic exchange interaction J1, the magnetization 〈Sz〉, the Curie temperature Tc and the magnetic susceptibility χ have been calculated by making use of the pair model approximation. It is pointed out that the biquadratic exchange interaction J1 gives different effects on the magnetization 〈Sz〉 of the Heisenberg ferromagnet and the Ising ferromagnet especially in the negative region of J1. Furthermore, it turns out that the Curie temperature for all anisotropic Heisenberg ferromagnets has nearly constant value for the biquadratic exchange interaction of J 1 = −J 10 .

We study antiferromagnetic, S=1/2 Heisenberg models with nearest- and second-neighbor interactions on the one-fifth-depleted square lattice which describes the spin degrees of freedom in the spin-gap system ${\mathrm{CaV}}_{4}$${\mathrm{O}}_{9}$. High-temperature expansions are used to calculate the temperature-dependent susceptibility, and Ising expansions are used to study phase boundaries and properties of the N\'eel-ordered phase, while plaquette and dimer expansions are used to calculate the ground-state properties and excitation spectra of magnetically disordered phases. The temperature dependences of the susceptibility and the spin gap are compared with experimental data on ${\mathrm{CaV}}_{4}$${\mathrm{O}}_{9}$. Within the parameter space we have considered, the data are best accounted for by a Hamiltonian in which the second-neighbor interactions are equal to (or perhaps somewhat less than) half the nearest-neighbor exchange, but the fits are not entirely satisfactory. The low-temperature triplet and singlet excitation spectra have many striking features which should be observable in neutron and Raman scattering experiments and would allow for more confident estimation of model parameters.

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.

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.

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.

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.

Stimulated by the small/large Fermi surface controversy in the cuprates, we consider a small number of holes injected into the bilayer antiferromagnet. The system has an $O(3)$ quantum critical point (QCP) separating the magnetically ordered and the magnetically disordered phases. We demonstrate that nearly critical quantum magnetic fluctuations can change the Fermi surface topology and also lead to spin charge separation (SCS) in two dimensions. We demonstrate that in the physically interesting regime there is a magnetically driven Lifshitz point (LP) inside the magnetically disordered phase. At the LP the topology of the hole Fermi surface is changed. The position of the LP, while being close to the position of the QCP, generally differs. Dependent on the additional hole hopping integrals ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{'}\ensuremath{'}}$, the LP can be located in the magnetically ordered phase and/or in the magnetically disordered phase. We also demonstrate that in this regime the hole spin and charge necessarily separate when approaching the QCP. The considered model sheds light on generic problems concerning the physics of the cuprates.

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.

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.}

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.

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