Discrete Hirota's equation in quantum integrable models

TL;DR

This paper reviews how classical integrable structures, specifically Hirota's bilinear difference equation, underpin quantum integrable models solved by Bethe ansatz, linking classical and quantum integrability.

Contribution

It demonstrates the connection between quantum transfer matrix eigenvalues and the classical Hirota equation, providing a new perspective on quantum integrability.

Findings

Fusion relations expressed via Hirota's equation

Generalization of Baxter's T-Q relation

Classical-quantum integrability link established

Abstract

The recent progress in revealing classical integrable structures in quantum models solved by Bethe ansatz is reviewed. Fusion relations for eigenvalues of quantum transfer matrices can be written in the form of classical Hirota's bilinear difference equation. This equation is also known as the completely discretized version of the 2D Toda lattice. We explain how one obtains the specific quantum results by solving the classical equation. The auxiliary linear problem for the Hirota equation is shown to generalize Baxter's T-Q relation.