Quantum Monte Carlo simulation method for spin systems

A quantum Monte Carlo simulation scheme for spin systems is presented. The method is a generalization of Handscomb's method but applicable to any length of the spin, i. e. , when the spin traces cannot be evaluated analytically. The Monte Carlo sampling is extended to the space of spin vectors in addition to the usual operator-index sequences. An important technical point is that the index sequences are augmented with the aid of unit operators to a constant, self-consistently determined length. The scheme is applied to the one-dimensional antiferromagnetic spin-S Heisenberg model. Results at low temperatures are reported for S=1 and S=3/2 and system sizes up to N=64. The computed magnetic structure factor in the S=1 chain is in agreement with earlier ground-state calculations. For S=3/2 we find the exponent =0. 490. 04 for the divergence of the antiferromagnetic structure factor. Further, the susceptibility as a function of the wave number is computed. For S=1 the staggered susceptibility () at T=0 is found to take the value 20. 01. 5 in units such that (q) T^-1 at high temperatures (with the temperature scale defined by k₁=1). For S=3/2 we obtain the exponent =1. 450. 05 for the divergence of the staggered susceptibility.