Quantum simulations of the superfluid-insulator transition for two-dimensional, disordered, hard-core bosons

We introduce two novel quantum Monte Carlo methods and employ them to study the superfluid-insulator transition in a two-dimensional system of hard-core bosons. One of the methods is appropriate for zero temperature and is based upon Green's function Monte Carlo; the other is a finite-temperature world-line cluster algorithm. In each case we find that the dynamical exponent is consistent with the theoretical prediction of $z=2$ by Fisher and co-workers.Comment: Revtex, 10 pages, 3 figures (postscript files attached at end, separated by %%%%%% Fig # %%%%%, where # is 1-3). LA-UR-94-270

Chaos in a Two-Dimensional Ising Spin Glass

We study chaos in a two dimensional Ising spin glass by finite temperature Monte Carlo simulations. We are able to detect chaos with respect to temperature changes as well as chaos with respect to changing the bonds, and find that the chaos exponents for these two cases are equal. Our value for the exponent appears to be consistent with that obtained in studies at zero temperature.Comment: 4 pages, LaTeX, 4 postscript figures included. The analysis of the data is now done somewhat differently. The results are consistent with the chaos exponent found at zero temperature. Additional papers of PY can be obtained on-line at http://schubert.ucsc.edu/pete

Generalization of the Fortuin-Kasteleyn transformation and its application to quantum spin simulations,

We generalize the Fortuin-Kasteleyn (FK) cluster representation of the partition function of the Ising model to represent the partition function of quantum spin models with an arbitrary spin magnitude in arbitrary dimensions. This generalized representation enables us to develop a new cluster algorithm for the simulation of quantum spin systems by the worldline Monte Carlo method. Because the Swendsen-Wang algorithm is based on the FK representation, the new cluster algorithm naturally includes it as a special case. As well as the general description of the new representation, we present an illustration of our new algorithm for some special interesting cases: the Ising model, the antiferromagnetic Heisenberg model with $S=1$, and a general Heisenberg model. The new algorithm is applicable to models with any range of the exchange interaction, any lattice geometry, and any dimensions.Comment: 46 pages, 10 figures, to appear in J.Stat.Phy

The Two-Dimensional S=1 Quantum Heisenberg Antiferromagnet at Finite Temperatures

The temperature dependence of the correlation length, susceptibilities and the magnetic structure factor of the two-dimensional spin-1 square lattice quantum Heisenberg antiferromagnet are computed by the quantum Monte Carlo loop algorithm (QMC). In the experimentally relevant temperature regime the theoretically predicted asymptotic low temperature behavior is found to be not valid. The QMC results however, agree reasonably well with the experimental measurements of La2NiO4 even without considering anisotropies in the exchange interactions.Comment: 4 Pages, 1 table, 4 figure

Quantum Monte Carlo Loop Algorithm for the t-J Model

We propose a generalization of the Quantum Monte Carlo loop algorithm to the t-J model by a mapping to three coupled six-vertex models. The autocorrelation times are reduced by orders of magnitude compared to the conventional local algorithms. The method is completely ergodic and can be formulated directly in continuous time. We introduce improved estimators for simulations with a local sign problem. Some first results of finite temperature simulations are presented for a t-J chain, a frustrated Heisenberg chain, and t-J ladder models.Comment: 22 pages, including 12 figures. RevTex v3.0, uses psf.te

Universality and universal finite-size scaling functions in four-dimensional Ising spin glasses

We study the four-dimensional Ising spin glass with Gaussian and bond-diluted bimodal distributed interactions via large-scale Monte Carlo simulations and show via an extensive finite-size scaling analysis that four-dimensional Ising spin glasses obey universality.Comment: 12 pages, 9 figures, 4 table

Kosterlitz-Thouless transition of quantum XY model in two dimensions

The two-dimensional $S=1/2$ XY model is investigated with an extensive quantum Monte Carlo simulation. The helicity modulus is precisely estimated through a continuous-time loop algorithm for systems up to $128 \times 128$ near and below the critical temperature. The critical temperature is estimated as $T_{\rm KT} = 0.3427(2)J$. The obtained estimates for the helicity modulus are well fitted by a scaling form derived from the Kosterlitz renormalization group equation. The validity of the Kosterlitz-Thouless theory for this model is confirmed.Comment: 8 pages, 2 tables, 6 figure

A New Method to Calculate the Spin-Glass Order Parameter of the Two-Dimensional +/-J Ising Model

A new method to numerically calculate the $n$th moment of the spin overlap of the two-dimensional $\pm J$ Ising model is developed using the identity derived by one of the authors (HK) several years ago. By using the method, the $n$th moment of the spin overlap can be calculated as a simple average of the $n$th moment of the total spins with a modified bond probability distribution. The values of the Binder parameter etc have been extensively calculated with the linear size, $L$, up to L=23. The accuracy of the calculations in the present method is similar to that in the conventional transfer matrix method with about $10^{5}$ bond samples. The simple scaling plots of the Binder parameter and the spin-glass susceptibility indicate the existence of a finite-temperature spin-glass phase transition. We find, however, that the estimation of $T_{\rm c}$ is strongly affected by the corrections to scaling within the present data ($L\leq 23$). Thus, there still remains the possibility that $T_{\rm c}=0$, contrary to the recent results which suggest the existence of a finite-temperature spin-glass phase transition.Comment: 10 pages,8 figures: final version to appear in J. Phys.