Numerical and Monte Carlo Bethe ansatz method: 1D Heisenberg model

TL;DR

This paper introduces two novel numerical methods for analyzing thermodynamic properties of integrable models like the 1D Heisenberg chain, demonstrating their effectiveness through comparisons with established techniques.

Contribution

The paper presents two new numerical approaches for studying thermodynamics in integrable models, validated against existing Bethe ansatz and Monte Carlo methods.

Findings

Results agree with thermodynamic Bethe ansatz

Results agree with Quantum Transfer Matrix

Effective for small and larger chains

Abstract

In this paper we present two new numerical methods for studying thermodynamic quantities of integrable models. As an example of the effectiveness of these two approaches, results from numerical solutions of all sets of Bethe ansatz equations, for small Heisenberg chains, and Monte Carlo simulations in quasi-momentum space, for a relatively larger chains, are presented. Our results agree with those obtained by thermodynamics Bethe ansatz (TBA) and Quantum Transfer Matrix (QTM).