Independent Bond Fluctuation Approximation to the Ground State of Quantum Antiferromagnets

TL;DR

This paper introduces a simple independent bond fluctuation approximation for estimating the ground state energy of quantum antiferromagnets, achieving results comparable to or better than spin wave theory, and offers insights into quantum spin fluctuations.

Contribution

It develops a novel approximation method assuming independent bond fluctuations, providing accurate energy estimates and correlations for quantum antiferromagnets.

Findings

Ground state energy estimates match or surpass spin wave theory.

The approach yields accurate spin correlations and dispersion relations.

The method can be extended to more complex models.

Abstract

A simple approach to estimation of the ground state energy of quantum antiferromagnets is developed, based on the approximation that quantum fluctuations around different bonds are independent. The ground state energy estimates are as good as spin wave theory or slightly better. A canonical transformation of the spin operators to generate bond quantum fluctuations is devised and applied to the classical ground state of the $S=\frac{1}{2}$ Heisenberg model on the square lattice. This simple picture of quantum spin fluctuations might be useful in more complex models. The resulting nearest neighbor and next-nearest neighbor correlations can be used in an alternative derivation of spin waves in the Heisenberg model, giving an accurate dispersion as well as raising and lowering operators.