O(1) contribution of saddle point fluctuations to the free energy of Bethe Ansatz systems

TL;DR

This paper introduces a method to compute saddle-point fluctuation contributions to the free energy in Bethe Ansatz solvable systems, providing O(1) corrections for models like the 1D delta Bose gas and XXZ chain.

Contribution

It presents a novel method for calculating O(1) saddle-point fluctuation corrections in Bethe Ansatz systems, applicable to various models.

Findings

Derived O(1) free energy corrections for 1D delta Bose gas

Extended the method to open boundary conditions and XXZ chain

Provided insights into fluctuation effects in integrable models

Abstract

We develop a method to calculate the contribution of the saddle-point fluctuations to the partition function of systems soluble by the Bethe Ansatz. Using this method we give the O(1) corrections to the free energy of the 1D repulsive delta Bose gas both for periodic boundary conditions and for the open end case. We also generalize our method to more complicated systems and discuss the case of XXZ Heisenberg chain in more details.