The free energy of anisotropic quantum spin systems: Functional integral representation

TL;DR

This paper introduces a functional integral approach to compute the free energy of anisotropic quantum spin systems, providing a series expansion and explicit formulas for Gaussian fluctuations, enhancing analytical tools in quantum magnetism.

Contribution

It develops a novel method using Hubbard-Stratonovich transformation for calculating free energy in anisotropic quantum spin systems, including series summation and fluctuation analysis.

Findings

Series representation for free energy in general models

Summation of series for Ising-type models

Explicit expression for Gaussian fluctuation contributions

Abstract

In this work, we propose a method for calculating the free energy of anisotropic quantum spin systems. We use the Hubbard-Stratonovich transformation to express the partition function of a generic bilinear super-exchange Hamiltonian in terms of a functional integral over classical time-dependent fields. In the general case the result is presented as an infinite series. The series may be summed up in the case of Ising-type models. For any ordered state we derive a compact expression for the contribution of Gaussian spin fluctuations to the free energy.