Ground state parameters, finite-size scaling, and low-temperature properties of the two-dimensional S=1/2 XY model

We present high-precision quantum Monte Carlo results for the S=1/2 XY model on a two-dimensional square lattice, in the ground state as well as at finite temperature. The energy, the spin stiffness, the magnetization, and the susceptibility are calculated and extrapolated to the thermodynamic limit. For the ground state, we test a variety of finite-size scaling predictions of effective Lagrangian theory and find good agreement and consistency between the finite-size corrections for different quantities. The low-temperature behavior of the susceptibility and the internal energy is also in good agreement with theoretical predictions.Comment: 6 pages, 8 figure

Critical and off-critical studies of the Baxter-Wu model with general toroidal boundary conditions

The operator content of the Baxter-Wu model with general toroidal boundary conditions is calculated analytically and numerically. These calculations were done by relating the partition function of the model with the generating function of a site-colouring problem in a hexagonal lattice. Extending the original Bethe-ansatz solution of the related colouring problem we are able to calculate the eigenspectra of both models by solving the associated Bethe-ansatz equations. We have also calculated, by exploring the conformal invariance at the critical point, the mass ratios of the underlying massive theory governing the Baxter-Wu model in the vicinity of its critical point.Comment: 32 pages latex, to appear in J. Phys. A: Math. Ge

Conformal invariance studies of the Baxter-Wu model and a related site-colouring problem

The partition function of the Baxter-Wu model is exactly related to the generating function of a site-colouring problem on a hexagonal lattice. We extend the original Bethe ansatz solution of these models in order to obtain the eigenspectra of their transfer matrices in finite geometries and general toroidal boundary conditions. The operator content of these models are studied by solving numerically the Bethe-ansatz equations and by exploring conformal invariance. Since the eigenspectra are calculated for large lattices, the corrections to finite-size scaling are also calculated.Comment: 12 pages, latex, to appear in J. Phys. A: Gen. Mat

Critical Behaviour of Structure Factors at a Quantum Phase Transition

We review the theoretical behaviour of the total and one-particle structure factors at a quantum phase transition for temperature T=0. The predictions are compared with exact or numerical results for the transverse Ising model, the alternating Heisenberg chain, and the bilayer Heisenberg model. At the critical wavevector, the results are generally in accord with theoretical expectations. Away from the critical wavevector, however, different models display quite different behaviours for the one-particle residues and structure factors.Comment: 17 pp, 10 figure

Series Expansions for three-dimensional QED

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 figure

A Frustrated 3-Dimensional Antiferromagnet: Stacked J1−J2J_{1}-J_{2} Layers

We study a frustrated 3D antiferromagnet of stacked $J_1 - J_2$ layers. The intermediate 'quantum spin liquid' phase, present in the 2D case, narrows with increasing interlayer coupling and vanishes at a triple point. Beyond this there is a direct first-order transition from N{\' e}el to columnar order. Possible applications to real materials are discussed.Comment: 11 pages,7 figure

Realization of a large J_2 quasi-2D spin-half Heisenberg system: Li2VOSiO4

Exchange couplings are calculated for Li2VOSiO4 using LDA. While the sum of in-plane couplings J_1 + J_2 = 9.5 \pm 1.5 K and the inter-plane coupling J_{perp} \sim 0.2 - 0.3 K agree with recent experimental data, the ratio J_2/J_1 \sim 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, Neel temperature and NMR spectra.Comment: 4 two-column pages, 4 embedded postscript figure

Stochastic series expansion method with operator-loop update

A cluster update (the ``operator-loop'') is developed within the framework of a numerically exact quantum Monte Carlo method based on the power series expansion of exp(-BH) (stochastic series expansion). The method is generally applicable to a wide class of lattice Hamiltonians for which the expansion is positive definite. For some important models the operator-loop algorithm is more efficient than loop updates previously developed for ``worldline'' simulations. The method is here tested on a two-dimensional anisotropic Heisenberg antiferromagnet in a magnetic field.Comment: 5 pages, 4 figure

Low energy states with different symmetries in the t-J model with two holes on a 32-site lattice

We study the low energy states of the t-J model with two holes on a 32-site lattice with periodic boundary conditions. In contrary to common belief, we find that the state with d_{x^2-y^2} symmetry is not always the ground state in the realistic parameter range 0.2\le J/t\le 0.4. There exist low-lying finite-momentum p-states whose energies are lower than the d_{x^2-y^2} state when J/t is small enough. We compare various properties of these low energy states at J/t=0.3 where they are almost degenerate, and find that those properties associated with the holes (such as the hole-hole correlation and the electron momentum distribution function) are very different between the d_{x^2-y^2} and p states, while their spin properties are very similar. Finally, we demonstrate that by adding ``realistic'' terms to the t-J model Hamiltonian, we can easily destroy the d_{x^2-y^2} ground state. This casts doubt on the robustness of the d_{x^2-y^2} state as the ground state in a microscopic model for the high temperature superconductors