Sign Rules for Anisotropic Quantum Spin Systems

TL;DR

This paper introduces exact sign rules for anisotropic quantum spin systems, enabling positive-definite ground-state wave functions after transformation, which improves the analysis of expectation values and computational methods.

Contribution

It provides new exact sign rules for anisotropic spin models and demonstrates their impact on understanding ground states and computational techniques.

Findings

Sign rules lead to positive-definite ground-state wave functions.

Transitions in expectation values occur at specific anisotropy points.

Sign rules enhance variational and quantum Monte Carlo calculations.

Abstract

We present new and exact ``sign rules'' for various spin-s anisotropic spin-lattice models. It is shown that, after a simple transformation which utilizes these sign rules, the ground-state wave function of the transformed Hamiltonian is positive-definite. Using these results exact statements for various expectation values of off-diagonal operators are presented, and transitions in the behavior of these expectation values are observed at particular values of the anisotropy. Furthermore, the effects of sign rules in variational calculations and quantum Monte Carlo calculations are considered. They are illustrated by a simple variational treatment of a one-dimensional anisotropic spin model.