Generalized T-Q relations and the open XXZ chain

TL;DR

This paper introduces a generalized T-Q relation for the open XXZ quantum spin chain, expanding the traditional relation to include multiple Q-functions, applicable under specific boundary conditions and anisotropy parameters.

Contribution

It proposes a novel generalized T-Q relation involving multiple Q-functions, applicable to the open XXZ chain with certain boundary parameters and anisotropy values.

Findings

Eigenvalues are described by the generalized T-Q relation.

Applicable when at most two boundary parameters are nonzero.

Valid for specific anisotropy values like   and  .

Abstract

We propose a generalization of the Baxter T-Q relation which involves more than one independent Q(u). We argue that the eigenvalues of the transfer matrix of the open XXZ quantum spin chain are given by such generalized T-Q relations, for the case that at most two of the boundary parameters {\alpha_-, \alpha_+, \beta_-, \beta_+} are nonzero, and the bulk anisotropy parameter has values \eta = i \pi/2, i\pi/4, ...