Generalized Integrable Boundary States in XXZ and XYZ Spin Chains

TL;DR

This paper generalizes the concept of integrable boundary states in XXZ and XYZ spin chains, providing explicit constructions and selection rules for eigenstates using the KT-relation.

Contribution

It introduces a generalized framework for integrable boundary states applicable to both XXZ and XYZ chains, including explicit state constructions and Bethe root selection rules.

Findings

Constructed factorized integrable boundary states for XXZ and XYZ chains.

Established a selection rule for Bethe roots based on boundary states.

Demonstrated the applicability of boundary states to different boundary conditions.

Abstract

We investigate integrable boundary states in the anisotropic Heisenberg chain under periodic or twisted boundary conditions, for both even and odd system lengths. Our work demonstrates that the concept of integrable boundary states can be readily generalized. For the XXZ spin chain, we present a set of factorized integrable boundary states using the KT-relation, and these states are also applicable to the XYZ chain. It is shown that a specific set of eigenstates of the transfer matrix can be selected by each boundary state, resulting in an explicit selection rule for the Bethe roots.