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

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

Accessing the dynamics of large many-particle systems using Stochastic Series Expansion

The Stochastic Series Expansion method (SSE) is a Quantum Monte Carlo (QMC) technique working directly in the imaginary time continuum and thus avoiding "Trotter discretization" errors. Using a non-local "operator-loop update" it allows treating large quantum mechanical systems of many thousand sites. In this paper we first give a comprehensive review on SSE and present benchmark calculations of SSE's scaling behavior with system size and inverse temperature, and compare it to the loop algorithm, whose scaling is known to be one of the best of all QMC methods. Finally we introduce a new and efficient algorithm to measure Green's functions and thus dynamical properties within SSE.Comment: 11 RevTeX pages including 7 figures and 5 table

Critical temperature and the transition from quantum to classical order parameter fluctuations in the three-dimensional Heisenberg antiferromagnet

We present results of extensive quantum Monte Carlo simulations of the three-dimensional (3D) S=1/2 Heisenberg antiferromagnet. Finite-size scaling of the spin stiffness and the sublattice magnetization gives the critical temperature Tc/J = 0.946 +/- 0.001. The critical behavior is consistent with the classical 3D Heisenberg universality class, as expected. We discuss the general nature of the transition from quantum mechanical to classical (thermal) order parameter fluctuations at a continuous Tc > 0 phase transition.Comment: 5 pages, Revtex, 4 PostScript figures include

Persistent superfluid phase in a three-dimensional quantum XY model with ring exchange

We present quantum Monte Carlo simulation results on a quantum S=1/2 XY model with ring exchange (the J-K model) on a three-dimensional simple cubic lattice. We first characterize the ground state properties of the pure XY model, obtaining estimations for the energy, spin stiffness and spin susceptibility at T=0 in the superfluid phase. With the ring exchange, we then present simulation data on small lattices which suggests that the superfluid phase persists to very large values of the ring exchange K, without signatures of a phase transition. We comment on the consequences of this result for the search for various exotic phases in three dimensions.Comment: 4 pages, 4 figure

NMR relaxation rates for the spin-1/2 Heisenberg chain

The spin-lattice relaxation rate $1/T_1$ and the spin echo decay rate $1/T_{2G}$ for the spin-$1\over 2$ antiferromagnetic Heisenberg chain are calculated using quantum Monte Carlo and maximum entropy analytic continuation. The results are compared with recent analytical calculations by Sachdev. If the nuclear hyperfine form factor $A_q$ is strongly peaked around $q=\pi$ the predicted low-temperature behavior [$1/T_1 \sim \ln{^{1/2}(1/T)}$, $1/T_{2G} \sim \ln{^{1/2}(1/T)}/\sqrt{T}$] extends up to temperatures as high as $T/J \approx 0.5$. If $A_q$ has significant weight for $q \approx 0$ there are large contributions from diffusive long-wavelength processes not taken into account in the theory, and very low temperatures are needed in order to observe the asymptotic $T \to 0$ forms.Comment: 9 pages, Revtex 3.0, 5 uuencoded ps figures To appear in Phys. Rev. B, Rapid Com