Twisted boundary energy and low energy excitation of the XXZ spin torus at the ferromagnetic region

TL;DR

This paper analyzes the thermodynamic limit of the ferromagnetic XXZ spin chain with twisted boundaries, revealing the Bethe root distribution, string hypothesis validity, and boundary energy effects.

Contribution

It demonstrates the string hypothesis applies to inhomogeneous Bethe Ansatz equations with twisted boundaries and computes the boundary energy in the thermodynamic limit.

Findings

Bethe root distribution follows the string hypothesis

String hypothesis holds despite inhomogeneous BAEs not being in standard form

Twisted boundary conditions induce a specific boundary energy

Abstract

We investigate the thermodynamic limit of the one-dimensional ferromagnetic XXZ model with twisted (or antiperiodic ) boundary condition. It is shown that the distribution of the Bethe roots of the inhomogeneous Bethe Ansatz equations (BAEs) for the ground state as well as for the low-lying excited states satisfy the string hypothesis, although the inhomogeneous BAEs are not in the standard product form which has made the study of the corresponding thermodynamic limit nontrivial. We also obtain the twisted boundary energy induced by the non-trivial twisted boundary conditions in the thermodynamic limit.