Relativistic Toda chain at root of unity II. Modified Q-operator

TL;DR

This paper explicitly constructs matrix elements and modified Q-operators for the quantum relativistic Toda chain at root of unity, linking quantum and classical integrability structures.

Contribution

It introduces explicit constructions of modified Q-operators that induce isospectrality transformations, connecting quantum and classical Bäcklund transformations.

Findings

Explicit matrix elements of quantum intertwiner and Q-operator provided.

Modified Q-operators induce classical Bäcklund isospectrality transformations.

Separated vectors for Bethe Ansatz constructed using modified Q-operators.

Abstract

Matrix elements of quantum intertwiner as well as the modified Q-operator for the quantum relativistic Toda chain at root of unity are constructed explicitly. Modified Q-operators make isospectrality transformations of quantum transfer matrices so that the classical counterparts of Q-operators correspond to the Baecklund isospectrality transformations of the classical transfer matrices. Separated vectors for the Functional Bethe Ansatz are constructed with the help of modified Q-operators.