Takahashi Integral Equation and High-Temperature Expansion of the Heisenberg Chain

TL;DR

This paper introduces a new integral equation for the 1D Heisenberg model, enabling high-temperature expansions of thermodynamic quantities up to order 100, surpassing previous methods and aiding low-temperature extrapolations.

Contribution

The paper presents a novel integral equation approach that allows for extremely high-order high-temperature expansions of the Heisenberg chain's thermodynamics.

Findings

High-temperature expansion of specific heat up to O((J/T)^{100})

High-temperature expansion of magnetic susceptibility up to O((J/T)^{100})

Results surpass standard methods like linked-cluster algorithm

Abstract

Recently a new integral equation describing the thermodynamics of the 1D Heisenberg model was discovered by Takahashi. Using the integral equation we have succeeded in obtaining the high temperature expansion of the specific heat and the magnetic susceptibility up to O((J/T)^{100}). This is much higher than those obtained so far by the standard methods such as the linked-cluster algorithm. Our results will be useful to examine various approximation methods to extrapolate the high temperature expansion to the low temperature region.