Droplet Excitations for the Spin-1/2 XXZ Chain with Kink Boundary Conditions

TL;DR

This paper rigorously defines droplet excitations in the spin-1/2 XXZ chain with various boundary conditions, proving their energies converge to a boundary condition independent value and deriving an explicit formula via Bethe ansatz.

Contribution

It introduces a precise definition of droplet excitations in the XXZ chain and computes their limiting energies explicitly using Bethe ansatz.

Findings

Droplet energies converge to a boundary condition independent value.

Explicit formula for the limiting droplet energy derived.

Rigorous proof of convergence in the thermodynamic limit.

Abstract

We give a precise definition for excitations consisting of a droplet of size n in the XXZ chain with various choices of boundary conditions, including kink boundary conditions and prove that, for each n, the droplet energies converge to a boundary condition independent value in the thermodynamic limit. We rigorously compute an explicit formula for this limiting value using the Bethe ansatz.