Reconstruction of Baxter Q-operator from Sklyanin SOV for cyclic representations of integrable quantum models

TL;DR

This paper reconstructs the Baxter Q-operator for cyclic representations of integrable quantum models using the Separation of Variables method, providing insights into spectrum characterization without relying on the direct construction of the Q-operator.

Contribution

It demonstrates how to derive the Baxter Q-operator solely from the SOV method for cyclic representations, extending the spectrum analysis approach.

Findings

Reconstructed Baxter Q-operator using SOV method

Characterized spectrum for cyclic representations

Extended spectrum analysis framework

Abstract

In [1], the spectrum (eigenvalues and eigenstates) of a lattice regularizations of the Sine-Gordon model has been completely characterized in terms of polynomial solutions with certain properties of the Baxter equation. This characterization for cyclic representations has been derived by the use of the Separation of Variables (SOV) method of Sklyanin and by the direct construction of the Baxter Q-operator family. Here, we reconstruct the Baxter Q-operator and the same characterization of the spectrum by only using the SOV method. This analysis allows us to deduce the main features required for the extension to cyclic representations of other integrable quantum models of this kind of spectrum characterization.