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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.

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 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.

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#

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.

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

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.

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 study the bipartite entanglement entropy of the 2D transverse-field Ising model in the thermodynamic limit. Series expansions are developed for the Renyi entropy around both the small-field and large-field limits, allowing the separate calculation of the entanglement associated with lines and corners at the boundary between subsystems. Series extrapolations are used to extract power laws and logarithmic singularities as the quantum critical point is approached, giving access to new universal quantities. In 1D, we find excellent agreement with exact results as well as quantum Monte Carlo simulations. In 2D, we find compelling evidence that the entanglement at a corner is significantly different from a free boson field theory. These results demonstrate the power of the series expansion method for calculating entanglement entropy in interacting systems, a fact that will be particularly useful in searches for exotic quantum criticality in models with and without the sign problem.

We demonstrate that nearly critical quantum magnetic fluctuations in strongly correlated electron systems can change the Fermi surface topology and also lead to spin charge separation (SCS) in two dimensions. To demonstrate these effects we consider a small number of holes injected into the bilayer antiferromagnet. The system has a quantum critical point (QCP) which separates magnetically ordered and disordered phases. 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. 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., Comment: updated version, accepted to PRL

We consider a three-dimensional quantum antiferromagnet which can be driven through a quantum critical point (QCP) by varying a tuning parameter $g$. Starting from the magnetically ordered phase, the N\'eel temperature will decrease to zero as the QCP is approached. From a generic quantum field theory, together with numerical results from a specific microscopic Heisenberg spin model, we demonstrate the existence of universal behavior near the QCP. We compare our results with available data for TlCuCl${}_{3}$.

Spin-wave approaches are explored for the spin-1 Heisenberg antiferromagnet with uniaxial single-ion anisotropy in a field. In the spin-flop region a standard $1/S$ expansion with canted quantization axes gives good results for small anisotropies or near the saturated ferromagnetic boundary. It is shown analytically that the formulation respects the Goldstone theorem through second order in $1/S$. For the square lattice case, we find that in the quantum paramagnetic phase a two-boson formulation gives good results at large anisotropies. Near the boundary of the quantum paramagnetic phase, neither approach gives good results and a more generalized approach is needed.

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.

Extended strong-coupling perturbation series are calculated for the vacuum energy and mass gaps of the U(1) and SU(2) lattice gauge theories in 2+1 dimensions. Extrapolating these series to the weak-coupling region, we estimate the scaling behavior for the antisymmetric mass gap of the U(1) model as {ital M}{sub {ital A}}{sup 2}{ital a2}=5.29(30){times}10{sup 2}{ital g{minus}2}exp({minus}5.42(6)/{ital g}{sup 2}), and the ratio of the symmetric mass gap ({ital M}{sub {ital S}}) to the antisymmetric mass gap ({ital M}{sub {ital A}}) is {ital M}{sub {ital S}}/{ital M}{sub {ital A}}=2.2(3). For the SU(2) model, the scaling behavior of the symmetric mass gap is {ital M}{sub {ital S}}{sup {ital a}}=2.22(5){ital g}{sup 2}{minus}0.38(4){ital g}{sup 4}. These results are in good agreement with theoretical expectations.

We revisit the problem of a single hole moving in the background of the two dimensional Heisenberg antiferromagnet. The hole is loosely bound by an impurity potential. We show that the bound state is generically a parity doublet: there are parametrically close bound states of opposite parity. Due to the degeneracy the bound state readily breaks local symmetries of the square lattice and this leads to formation of the long range spiral distortion of the antiferromagnetic background. A direct analogy with van der Waals forces in atomic physics is discussed.

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.

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.

We present a detailed description of the dynamics of the magnetic modes in the recently discovered superconducting pnictides using reliable self-consistent spin-wave theory and series expansion. Contrary to linear spin-wave theory, no gapless mode occurs at the N\'eel wave vector. We discuss the scenario that the static magnetic moment is strongly reduced by magnetic fluctuations arising from the vicinity to a quantum phase transition. Smoking gun experiments to verify this scenario are proposed and possible results are predicted. Intriguingly in this scenario, the structural transition at finite temperature would be driven by an Ising transition in directional degrees of freedom., Comment: 5 pages, 4 figures, to appear in Phys. Rev. B

We calculate ground state properties (energy, magnetization, susceptibility) and one-particle spectra for the $S=1$ Heisenberg antiferromagnet with easy-axis or easy-plane single-site anisotropy on the square lattice. Series expansions are used, in each of three phases of the system, to obtain systematic and accurate results. The location of the quantum phase transition in the easy-plane sector is determined. The results are compared to spin-wave theory.

We present numerical results for an $S=1/2$ Heisenberg antiferromagnet on a inhomogeneous square lattice with tunable interaction between spins belonging to different plaquettes. Employing Quantum Monte Carlo, we significantly improve on previous results for the the critical point separating singlet-disordered and N\'{e}el-ordered phases, and obtain an estimate for the critical exponent $\nu$ consistent with the three-dimensional classical Heisenberg universality class. Additionally, we show that a fairly accurate result for the critical point can be obtained from a Contractor Renormalization (CORE) expansion by applying a surprisingly simple analysis to the effective Hamiltonian., Comment: 4+ pages, 3 figures. Published version

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.

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

We have extended our previous series studies of quantum antiferromagnets at zero temperature by computing the one-magnon dispersion curves and various structure factors for the linear chain, square and simple cubic lattices. Many of these results are new; others are a substantial extension of previous work. These results are directly comparable with neutron scattering experiments and we make such comparisons where possible.

The large ${J}_{2}$ limit of the square-lattice ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg antiferromagnet is a classic example of order by disorder where quantum fluctuations select a collinear ground state. Here, we use series expansion methods and a mean-field spin-wave theory to study the excitation spectra in this phase and look for a finite-temperature Ising-like transition, corresponding to a broken symmetry of the square lattice, as first proposed by Chandra et al. [Phys. Rev. Lett. 64, 88 (1990)]. We find that the spectra reveal the symmetries of the ordered phase. However, we do not find evidence for a finite-$T$ transition. We suggest a scenario for a $T=0$ transition based on quantum fluctuations.

We present results for the Kondo lattice model of strongly correlated electrons, in one, two, and three dimensions, obtained from high-order linked-cluster series expansions. Results are given for various ground-state properties at half filling, and for spin and charge excitations. Estimates for the location of the quantum critical point in the square and simple cubic lattices are made.

We investigate a ferromagnetic spin-1 Ising model with a transverse single-ion crystal-field term. By means of a mapping to the usual spin-1/2 transverse Ising model, we determine the location of the $T=0$ quantum critical point exactly in one dimension, and to high precision in higher dimensions. The nature of the excited states is also explored. We show how this approach can be generalized to higher spin values.

We use perturbative series expansions about a staggered dimerized ground state to compute the ground state energy, triplet excitation spectra and spectral weight for a one-dimensional model in which each site has an $S=\case 1/2$ spin ${\bf S}_i$ and a pseudospin ${\bf T}_i$, representing a doubly degenerate orbital. An explicit dimerization is introduced to allow study of the confinement of spinon excitations. The elementary triplet represents a bound state of two spinons, and is stable over much of the Brillouine zone. A special line is found in the gapped spin-liquid phase, on which the triplet excitation is dispersionless. The formation of triplet bound states is also investigated., 9 pages, 9 figures

We study the phase diagram of the spin-orbital model in both the weak and strong limits of the quartic spin-orbital exchange interaction. This allows us to study quantum phase transitions in the model and to approach from both sides the most interesting intermediate-coupling regime and in particular the SU(4)-symmetric point of the Hamiltonian. It was suggested earlier by Li et al [Phys.Rev.Lett. vol. 81, 3527 (1999)] that at this point the ground state of the system is a plaquette spin-orbital liquid. We argue that the state is more complex. There is plaquette order, but it is anisotropic: bonds in one direction are stronger than those in the perpendicular direction. This order is somewhat similar to that found recently in the frustrated J_1-J_2 Heisenberg spin model., 8 pages, 4 Postscript figures

We investigate the properties of S=1/2 Heisenberg clusters with random frustration using exact diagonalizations. This is a model for a quantum spin glass. We show that the average ground state spin is $S \propto \sqrt{N}$, where N is the number of sites. We also calculate the magnetic susceptibility and the spin stiffness and low-energy excitations, and discuss these in terms of a semiclassical picture., Comment: 4 pages, 3 figures, 2 tables

We overview some recent work and present new results on the ground state properties and the spectrum of excitations of the two-dimensional frustrated Heisenberg antiferromagnet. Spontaneous dimer order is present in the quantum disordered phase of this model. We study the stability and analyze the structure of the spectrum, including the two-particle singlet excitation branch throughout the disordered phase, as well as in the vicinity of the Neel critical point. The variation of the dimer order parameter is also given, and it is argued that near the critical point it reflects the presence of the low-energy singlet bound state., 20 pages, 9 figures. Extended version of the invited talk, presented at the ITP Conference on Quantum Magnetism, Santa Barbara, August 1999

We consider quantum spin systems with dimerization, which at strong coupling have singlet ground states. To account for strong correlations, the excitations are described as dilute Bose gas of degenerate triplets with infinite on-site repulsion. This approach is applied to the two-layer Heisenberg model at zero temperature with general couplings. Our analytic results for the triplet gap, the excitation spectrum and the location of the quantum critical point are in excellent agreement with numerical results, obtained by dimer series expansions., Comment: 4 pages, REVTex, 3 Postscript figures

Spin-S bilayer Heisenberg models (nearest-neighbor square lattice antiferromagnets in each layer, with antiferromagnetic interlayer couplings) are treated using dimer mean-field theory for general S and high-order expansions about the dimer limit for S=1, 3/2,...,4. We suggest that the transition between the dimer phase at weak intraplane coupling and the Neel phase at strong intraplane coupling is continuous for all S, contrary to a recent suggestion based on Schwinger boson mean-field theory. We also present results for S=1 layers based on expansions about the Ising limit: In every respect the S=1 bilayers appear to behave like S=1/2 bilayers, further supporting our picture for the nature of the order-disorder phase transition., Comment: 6 pages, Revtex 3.0, 8 figures (not embedded in text)

Linked cluster methods are used to calculate extended strong-coupling series expansions for the ground-state energy, specific heat, scalar, and axial-vector mass gaps in the [ital Z][sub [ital N]] and U(1) Abelian gauge models in 3+1 dimensions. There is evidence of a singularity at physical couplings in the specific heat series, but none in the mass gap series. A comparison with Monte Carlo data in the U(1) case indicates that there is actually a weak first-order transition.

The authors investigate the properties of ferromagnetic spin systems with higher-order exchange interactions, in particular with four-spin terms of the form (Si.Sj)(Sk.Sl) and (Si.Sj)(Sj.Sk). Using the Green function equation of motion method, and simple decoupling approximations, they obtain renormalised spin-wave energies, magnetisation curves, and critical temperatures for various strengths of the four-spin interactions. For sufficiently large values of these interactions the transition becomes first order. For comparison they also give the results of spin-wave and mean-field theories.

A biquadratic Heisenberg ferromagnet with Hamiltonian H=- mu H Sigma bSbz- Sigma abJab(Sa.Sb)- Sigma ab alpha Jab(Sa.Sb)2 is investigated with a simple Green function approach. Some invalid results of earlier treatments are noted and magnetization curves are presented for spin-1 in a simple cubic lattice. Comparison is made with mean field and constant coupling results. The phase transition is found to be second order for alpha 0.48.

The high temperature susceptibility series of the model proposed by Haus and Tanaka (1977) to account for the transition of the orientationally disordered ice VII phase to the orientationally ordered ice VIII phase does not provide evidence for the possible occurrence of a first-order transition, as predicted by the mean field approximation, but gives a second-order transition instead.