The master T-operator for vertex models with trigonometric $R$-matrices as classical tau-function
Abstract
The construction of the master T-operator recently suggested in Alexandrov et al. (arXiv:1112.3310) is applied to integrable vertex models and associated quantum spin chains with trigonometric R-matrices. The master T-operator is a generating function for commuting transfer matrices of integrable vertex models depending on infinitely many parameters. At the same time it turns out to be the tau-function of an integrable hierarchy of classical soliton equations in the sense that it satisfies the the same bilinear Hirota equations. The class of solutions of the Hirota equations that correspond to eigenvalues of the master T-operator is characterized and its relation to the classical Ruijsenaars-Schneider system of particles is discussed.
Cite
@article{arxiv.1205.4152,
title = {The master T-operator for vertex models with trigonometric $R$-matrices as classical tau-function},
author = {A. Zabrodin},
journal= {arXiv preprint arXiv:1205.4152},
year = {2015}
}
Comments
19 pages, for proceedings of the workshop "Classical and Quantum Integrable Systems" (Dubna, 23-27 January 2012), typos corrected