Kink confinement in the antiferromagnetic XXZ spin-1/2 chain in a weak staggered magnetic field

TL;DR

This paper investigates how a weak staggered magnetic field causes confinement of kinks in the antiferromagnetic XXZ spin-1/2 chain, leading to bound states, with perturbative calculations in the Ising limit and for generic anisotropy.

Contribution

It provides the first perturbative analysis of kink confinement and bound state spectra in the XXZ chain under a weak staggered magnetic field, extending understanding beyond integrable cases.

Findings

Confinement induces bound states of kinks in the model.

Perturbative spectra are obtained in the Ising limit and for general anisotropy.

The magnetic field breaks integrability, leading to long-range attractive interactions.

Abstract

The Heisenberg XXZ spin-1/2 chain is considered in the massive antiferromagnetic regime in the presence of a staggered longitudinal magnetic field. The Hamiltonian of the model is characterised by the anisotropy parameter $\Delta<-1$, and by the magnetic field strength h. At zero magnetic field, the model is exactly solvable. In the thermodynamic limit, it has two degenerate vacua and the kinks (which are also called spinons) interpolating between these vacua, as elementary excitations. Application of the staggered magnetic field breaks integrability of the model and induces the long-range attractive potential between two adjacent kinks leading to their confinement into the bound states. The energy spectra of the resulting two-kink bound states are perturbatively calculated in the extreme anisotropic (Ising) limit $\Delta\to-\infty$ to the first order in the inverse anisotropy constant $|\Delta|^{-1}$, and also for generic values of $\Delta<-1$ to the first order in the weak magnetic field h.