Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II

J. M. Maillet, G. Niccoli, B. Pezelier

SciPost Phys. 5, 026 (2018) · published 24 September 2018

Abstract

This article is a direct continuation of [1] where we begun the study of the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazhanov-Stroganov Lax operator. There we addressed this problem for the case where one of the K-matrices describing the boundary conditions is triangular. In the present article we consider the most general integrable boundary conditions, namely the most general boundary K-matrices satisfying the reflection equation. The spectral analysis is developed by implementing the method of Separation of Variables (SoV). We first design a suitable gauge transformation that enable us to put into correspondence the spectral problem for the most general boundary conditions with another one having one boundary K-matrix in a triangular form. In these settings the SoV resolution can be obtained along an extension of the method described in [1]. The transfer matrix spectrum is then completely characterized in terms of the set of solutions to a discrete system of polynomial equations in a given class of functions and equivalently as the set of solutions to an analogue of Baxter's T-Q functional equation. We further describe scalar product properties of the separate states including eigenstates of the transfer matrix.

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Algebraic Bethe Ansatz (ABA) Baxter T-Q equation Bazhanov-Stroganov model Boundary K-matrices Integrable boundary conditions Lax operators Reflection algebra Separation of Variables (SoV) method Spectral analysis Transfer matrix

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