Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain

TL;DR

This paper constructs the Baxter Q-operator and the separated variables representation for the open SL(2,R) spin chain, solving its spectral problem and revealing a universal factorized transition kernel structure.

Contribution

It introduces a novel construction of the Baxter Q-operator and the SoV representation for the open SL(2,R) spin chain, extending the understanding of integrable models.

Findings

Calculated Sklyanin's integration measure in SoV

Obtained spectral solution via Q-operator eigenvalues

Discovered universal pyramid-like transition kernel form

Abstract

We construct the Baxter Q-operator and the representation of the Separated Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the diagrammatical approach, we calculate Sklyanin's integration measure in the separated variables and obtain the solution to the spectral problem for the model in terms of the eigenvalues of the Q-operator. We show that the transition kernel to the SoV representation is factorized into the product of certain operators each depending on a single separated variable. As a consequence, it has a universal pyramid-like form that has been already observed for various quantum integrable models such as periodic Toda chain, closed SL(2,R) and SL(2,C) spin chains.