SciPost Physics

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

• doi: 10.21468/SciPostPhys.5.3.026
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

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.

• Maillet et al., On separation of variables for reflection algebras
  J. Stat. Mech. 2019, 094020 (2019) [Crossref]
• Kitanine et al., The open XXZ spin chain in the SoV framework: scalar product of separate states
  J. Phys. A: Math. Theor. 51, 485201 (2018) [Crossref]
• Maillet et al., Separation of variables bases for integrable $gl_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
  SciPost Phys. 9, 060 (2020) [Crossref]
• Maillet et al., On quantum separation of variables beyond fundamental representations
  SciPost Phys. 10, 026 (2021) [Crossref]
• Maillet et al., Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
  SciPost Phys. 6, 071 (2019) [Crossref]
• Maillet et al., On scalar products in higher rank quantum separation of variables
  SciPost Phys. 9, 086 (2020) [Crossref]