Generation of a quantum integrable class of discrete-time or relativistic periodic Toda chains

TL;DR

This paper introduces a new integrable quantum class of models generalizing the periodic Toda chain, including discrete-time and relativistic variants, derived from a single ancestor model ensuring quantum integrability.

Contribution

It presents a unified framework for a class of quantum integrable models related to the Toda chain, with explicit Lax operators and R-matrices derived from a common ancestor.

Findings

All models are obtainable from a single ancestor model.

Explicit Lax operators and R-matrices are derived, ensuring integrability.

The Bethe ansatz for the Toda chain extends to these models.

Abstract

A new integrable class of quantum models representing a family of different discrete-time or relativistic generalisations of the periodic Toda chain (TC), including that of a recently proposed classical close to TC model [7] is presented. All such models are shown to be obtainable from a single ancestor model at different realisations of the underlying quantised algebra. As a consequence the $(2\times 2)$ Lax operators and the associated quantum $R$-matrices for these models are easily derived ensuring their quantum integrability. It is shown that the functional Bethe ansatz developed for the quntum TC is trivially generalised to achieve seperation of variables also for the present models.