Thermodynamic limit and twisted boundary energy of the XXZ spin chain with antiperiodic boundary condition

TL;DR

This paper analyzes the thermodynamic limit of the XXZ spin chain with antiperiodic boundary conditions, showing the inhomogeneous term's contribution vanishes at large sizes, simplifying the Bethe ansatz equations and enabling energy calculations.

Contribution

It demonstrates that the inhomogeneous term can be neglected in the thermodynamic limit, simplifying the analysis of the XXZ spin chain with antiperiodic boundary conditions.

Findings

Inhomogeneous term negligible at large N

Homogeneous Bethe ansatz equations applicable in thermodynamic limit

Calculated twisted boundary energy for the system

Abstract

We investigate the thermodynamic limit of the inhomogeneous T-Q relation of the antiferromagnetic XXZ spin chain with antiperiodic boundary condition. It is shown that the contribution of the inhomogeneous term at the ground state can be neglected when the system-size N tends to infinity, which enables us to reduce the inhomogeneous Bethe ansatz equations (BAEs) to the homogeneous ones. Then the quantum numbers at the ground states are obtained, by which the system with arbitrary size can be studied. We also calculate the twisted boundary energy of the system.