Dynamic Scaling in the Two-Dimensional Heisenberg Antiferromagnet

Abstract

The two-dimensional Heisenberg antiferromagnet has generated considerable interest with respect to its applications for understanding copper-oxide -based high temperature superconductors.¹ The model is described by a Hamiltonian,

$$H = J\sum\limits_{\left( {n,m} \right)} {{{\vec S}_n}{{\vec S}_m}}$$

((1))

where J > 0 and the sum is over nearest neighbor spin variables S_n. While analytic calculations of either ground state or dynamic properties are very difficult for this and related nonlinear spin models, it is sometimes possible to extract important information from numerical calculations. Some success in obtaining ground state properties for the spin-1/2 model has resulted from quantum Monte Carlo calculations.² However, the principle interest here is in dynamics, for which quantum Monte Carlo calculations are emerging but not yet well-developed. Nevertheless, progress in obtaining quantities such as the dynamic structure function S(q,ω) is occuring.³