Confinement of spinons in the XXZ spin-1/2 chain in presence of the transverse magnetic field

TL;DR

This paper investigates how a transverse magnetic field influences spinon confinement in the XXZ spin-1/2 chain, providing analytical calculations of two-spinon bound states and their effects on dynamical structure factors.

Contribution

It introduces two perturbative schemes to analytically study the energy spectra of spinon bound states under transverse magnetic fields in the XXZ chain.

Findings

Weak transverse magnetic field causes mixing of meson modes.

Avoided crossing of meson energies occurs with increasing field.

Explicit formulas for dynamical structure factors are derived.

Abstract

We study the tuning effect of a transverse magnetic field on the confinement of spinons in the infinite XXZ spin-1/2 chain. The spinon confinement in this model takes place in the gapped antiferromagnetic phase upon application of a staggered longitudinal magnetic field. The tuning transverse magnetic field has mutually orthogonal uniform and staggered components. The energy spectra of the two-spinon bound states (the `mesons') in the confinement regime are analytically calculated in this model using two different perturbative schemes. The first one applies in the extreme anisotropic (Ising) limit and employs the inverse anisotropy constant as a small parameter. The second perturbative scheme, which applies at any anisotropy in the gapped antiferromagnetic domain, exploits the integrability of the XXZ spin chain at zero magnetic field. The small parameters in the second technique are the components of the transverse, and staggered longitudinal magnetic fields. It is shown, that the weak transverse magnetic field mixes the transverse and longitudinal meson modes, and leads to an avoided crossing of their energies upon increase of its strength. The explicit formulas for the two-spinon contribution to the dynamical structure factors of local spin operators are obtained as well in this model in the weak confinement regime for wave-vectors close to the points k = 0 and k = \pi.