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-Peierls transition in the Heisenberg chain with finite-frequency phonons

We study the spin-Peierls transition in a Heisenberg spin chain coupled to optical bond phonons. Quantum Monte Carlo results for systems with up to N=256 spins show unambiguously that the transition occurs only when the spin-phonon coupling α exceeds a critical value α_c. Using sum rules, we show that the phonon spectral function has divergent (for N→∞) weight extending to zero frequency for α<α_c. The phonon correlations decay with distance r as 1/r. This behavior is characteristic for all 0<α<α_c and the q=π phonon does not soften (to zero frequency) at α=α_c.First author draf

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

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

Impurity effects at finite temperature in the two-dimensional S=1/2 Heisenberg antiferromagnet

We discuss effects of various impurities on the magnetic susceptibility and the specific heat of the quantum S=1/2 Heisenberg antiferromagnet on a two-dimensional square lattice. For impurities with spin S_i > 0 (here S_i=1/2 in the case of a vacancy or an added spin, and S_i=1 for a spin coupled ferromagnetically to its neighbors), our quantum Monte Carlo simulations confirm a classical-like Curie susceptibility contribution S_i^2/4T, which originates from an alignment of the impurity spin with the local N\'eel order. In addition, we find a logarithmically divergent contribution, which we attribute to fluctuations transverse to the local N\'eel vector. We also study frustrated and nonfrustrated bond impurities with S_i=0. For a simple intuitive picture of the impurity problem, we discuss an effective few-spin model that can distinguish between the different impurities and reproduces the leading-order simulation data over a wide temperature range.Comment: 15 pages, 14 figures, submitted to PRB. v2, published version with cosmetic change

Coarse-grained loop algorithms for Monte Carlo simulation of quantum spin systems

Recently, Syljuasen and Sandvik proposed a new framework for constructing algorithms of quantum Monte Carlo simulation. While it includes new classes of powerful algorithms, it is not straightforward to find an efficient algorithm for a given model. Based on their framework, we propose an algorithm that is a natural extension of the conventional loop algorithm with the split-spin representation. A complete table of the vertex density and the worm-scattering probability is presented for the general XXZ model of an arbitrary S with a uniform magnetic field.Comment: 12 pages, 7 figures, insert a word "squared" in the first line of the caption of Fig.7 and correct the label of vertical axis of Fig.