Graphical representation of the partition function for a 1-D delta-function Bose gas

TL;DR

This paper derives exact n-particle partition functions for a 1-D delta-function Bose gas using Bethe ansatz, confirming the validity of the thermal Bethe ansatz through a graphical and partition-based approach.

Contribution

It provides an exact calculation of partition functions and cluster integrals for the 1-D Bose gas, validating the thermal Bethe ansatz with a novel graphical method.

Findings

Exact n-particle partition functions match TBA results

Cluster integrals derived directly from Bethe ansatz

Graphical and partition methods simplify the analysis

Abstract

One-dimensional repulsive delta-function bose system is studied. By only using the Bethe ansatz equation, n-particle partition functions are exactly calculated. From this expression for the n-particle partition function, the n-particle cluster integral is derived. The results completely agree with those of the thermal Bethe ansatz (TBA). This directly proves the validity of the TBA. The theory of partitions and graphs is used to simplify the discussion.