KP and Toda tau functions in Bethe ansatz

TL;DR

This paper reviews the connection between classical integrable hierarchies, specifically KP and Toda tau functions, and quantum integrable systems like the 6-vertex model and XXZ chain, highlighting recent developments.

Contribution

It synthesizes recent research linking classical integrable hierarchies with quantum integrable models, emphasizing the role of tau functions in this correspondence.

Findings

Identification of KP and Toda tau functions with quantum system partition functions

Clarification of the mathematical structure underlying quantum integrable models

Extension of classical-quantum integrability connections

Abstract

Recent work of Foda and his group on a connection between classical integrable hierarchies (the KP and 2D Toda hierarchies) and some quantum integrable systems (the 6-vertex model with DWBC, the finite XXZ chain of spin 1/2, the phase model on a finite chain, etc.) is reviewed. Some additional information on this issue is also presented.