Monte--Carlo Thermodynamic Bethe Ansatz

TL;DR

This paper presents a Monte-Carlo simulation method for thermodynamic Bethe ansatz, enabling precise calculation of central charges, energies, and partition functions in integrable models, including free particles and the Lee-Yang model.

Contribution

It introduces a novel Monte-Carlo approach to TBA that improves the calculation of thermodynamic quantities in integrable models.

Findings

Accurately computes central charges and energies to about 0.1%

Successfully applies to free boson, fermion, and Lee-Yang models

Enables calculation of all dimensions and partition functions

Abstract

We introduce a Monte--Carlo simulation approach to thermodynamic Bethe ansatz (TBA). We exemplify the method on one particle integrable models, which include a free boson and a free fermions systems along with the scaling Lee--Yang model (SLYM). It is confirmed that the central charges and energies are correct to a very good precision, typically 0.1% or so. The advantage of the method is that it enables the calculation of all the dimensions and even the particular partition function.