Efficient Thermodynamic Description of Multi-Component One-Dimensional Bose Gases

TL;DR

This paper introduces a new, efficient method using nonlinear integral equations and quantum transfer matrices to describe the thermodynamics of multi-component one-dimensional Bose gases, simplifying previous approaches.

Contribution

The authors develop a simplified system of nonlinear integral equations for multi-component Bose gases, improving computational efficiency over traditional Thermodynamic Bethe Ansatz methods.

Findings

Efficient numerical implementation for two-component Bose gases.

Reduction of infinite coupled equations to a manageable system.

Application of quantum transfer matrix techniques to continuum gases.

Abstract

We present a new method of obtaining nonlinear integral equations characterizing the thermodynamics of one-dimensional multi-component gases interacting via a delta-function potential. In the case of the repulsive two-component Bose gas we obtain a simple system of two NLIE allowing for an efficient numerical implementation in contrast with the infinite number of coupled equations obtained by employing the Thermodynamic Bethe Ansatz. Our technique makes use of the Quantum Transfer Matrix and the fact that in a certain continuum limit multi-component gases can be obtained from appropriate anisotropic spin chains.