Comment on ``Quantum Phase Transition of the Randomly Diluted Heisenberg Antiferromagnet on a Square Lattice''

In Phys. Rev. Lett. 84, 4204 (2000) (cond-mat/9905379), Kato et al. presented quantum Monte Carlo results indicating that the critical concentration of random non-magnetic sites in the two-dimensional antiferromagnetic Heisenberg model equals the classical percolation density; pc=0.407254. The data also suggested a surprising dependence of the critical exponents on the spin S of the magnetic sites, with a gradual approach to the classical percolation exponents as S goes to infinity. I here argue that the exponents in fact are S-independent and equal to those of classical percolation. The apparent S-dependent behavior found by Kato et al. is due to temperature effects in the simulations as well as a quantum effect that masks the true asymptotic scaling behavior for small lattices.Comment: Comment on Phys. Rev. Lett. 84, 4204 (2000), by K. Kato et al.; 1 page, 1 figur

Loop updates for variational and projector quantum Monte Carlo simulations in the valence-bond basis

We show how efficient loop updates, originally developed for Monte Carlo simulations of quantum spin systems at finite temperature, can be combined with a ground-state projector scheme and variational calculations in the valence bond basis. The methods are formulated in a combined space of spin z-components and valence bonds. Compared to schemes formulated purely in the valence bond basis, the computational effort is reduced from up to O(N^2) to O(N) for variational calculations, where N is the system size, and from O(m^2) to O(m) for projector simulations, where m>> N is the projection power. These improvements enable access to ground states of significantly larger lattices than previously. We demonstrate the efficiency of the approach by calculating the sublattice magnetization M_s of the two-dimensional Heisenberg model to high precision, using systems with up to 256*256 spins. Extrapolating the results to the thermodynamic limit gives M_s=0.30743(1). We also discuss optimized variational amplitude-product states, which were used as trial states in the projector simulations, and compare results of projecting different types of trial states.Comment: 12 pages, 9 figures. v2: Significantly expanded, to appear in Phys. Rev.

Spin nematic ground state of the triangular lattice S=1 biquadratic model

Motivated by the spate of recent experimental and theoretical interest in Mott insulating S=1 triangular lattice magnets, we consider a model S=1 Hamiltonian on a triangular lattice interacting with rotationally symmetric biquadratic interactions. We show that the partition function of this model can be expressed in terms of configurations of three colors of tightly-packed, closed loops with {\em non-negative} weights, which allows for efficient quantum Monte Carlo sampling on large lattices. We find the ground state has spin nematic order, i.e. it spontaneously breaks spin rotation symmetry but preserves time reversal symmetry. We present accurate results for the parameters of the low energy field theory, as well as finite-temperature thermodynamic functions

Order-Disorder Transition in a Two-Layer Quantum Antiferromagnet

We have studied the antiferromagnetic order -- disorder transition occurring at $T=0$ in a 2-layer quantum Heisenberg antiferromagnet as the inter-plane coupling is increased. Quantum Monte Carlo results for the staggered structure factor in combination with finite-size scaling theory give the critical ratio $J_c = 2.51 \pm 0.02$ between the inter-plane and in-plane coupling constants. The critical behavior is consistent with the 3D classical Heisenberg universality class. Results for the uniform magnetic susceptibility and the correlation length at finite temperature are compared with recent predictions for the 2+1-dimensional nonlinear $\sigma$-model. The susceptibility is found to exhibit quantum critical behavior at temperatures significantly higher than the correlation length.Comment: 11 pages (5 postscript figures available upon request), Revtex 3.

Monte Carlo Simulations of Quantum Spin Systems in the Valence Bond Basis

We discuss a projector Monte Carlo method for quantum spin models formulated in the valence bond basis, using the S=1/2 Heisenberg antiferromagnet as an example. Its singlet ground state can be projected out of an arbitrary basis state as the trial state, but a more rapid convergence can be obtained using a good variational state. As an alternative to first carrying out a time consuming variational Monte Carlo calculation, we show that a very good trial state can be generated in an iterative fashion in the course of the simulation itself. We also show how the properties of the valence bond basis enable calculations of quantities that are difficult to obtain with the standard basis of Sz eigenstates. In particular, we discuss quantities involving finite-momentum states in the triplet sector, such as the dispersion relation and the spectral weight of the lowest triplet.Comment: 15 pages, 7 figures, for the proceedings of "Computer Simulation Studies in Condensed Matter Physics XX