A New Method of the High Temperature Series Expansion

TL;DR

This paper introduces a novel method for high-temperature series expansions applicable to SU(n) Heisenberg models, extending finite cluster techniques and emphasizing combinatorial and cumulant-based calculations.

Contribution

It presents a new cumulant-based approach that improves the efficiency of calculating high-temperature series and correlation functions for complex spin models.

Findings

Series coefficients expressed via cumulants and quasi-moments.

Efficient calculation of correlation functions at widely separated sites.

New technique for low-order specific heat contributions from finite clusters.

Abstract

We formulate a new method of performing high-temperature series expansions for the spin-half Heisenberg model or, more generally, for SU($n$) Heisenberg model with arbitrary $n$. The new method is a novel extension of the well-established finite cluster method. Our method emphasizes hidden combinatorial aspects of the high-temperature series expansion, and solves the long-standing problem of how to efficiently calculate correlation functions of operators acting at widely separated sites. Series coefficients are expressed in terms of cumulants, which are shown to have the property that all deviations from the lowest-order nonzero cumulant can be expressed in terms of a particular kind of moment expansion. These ``quasi-moments'' can be written in terms of corresponding ``quasi-cumulants'', which enable us to calculate higher-order terms in the high-temperature series expansion. We also present a new technique for obtaining the low-order contributions to specific heat from finite clusters.