Scaling limit of the one-dimensional XXZ Heisenberg chain with easy axis anisotropy

TL;DR

This paper constructs the scaling limit of the one-dimensional easy axis XXZ Heisenberg chain, revealing its excitation spectrum, energy gaps, and underlying SU(2) symmetry through Bethe Ansatz analysis.

Contribution

It provides a detailed analysis of the scaling limit of the easy axis XXZ chain, including the spectrum structure and symmetry properties, using Bethe Ansatz techniques.

Findings

Energy difference between vacua quantified

Excitations form two distinct sets with Bethe Ansatz equations

Spectrum degeneracies linked to SU(2) symmetry

Abstract

We construct the scaling limit of the easy axis XXZ chain. This limit is a subtle combination of approaching the isotropic point, and letting the lattice spacing to zero to obtain a continuous model with a finite mass gap. We give the energy difference between the two lowest energy states (the two `vacua') and analyze the structure of the excitation spectrum of the limiting model. We find, that the excitations form two sets corresponding to the two vacua. In both sets the dressed particles are described by Bethe Ansatz like equations (higher level Bethe Ansatz), and the two sets can be distinguished through a parameter entering into these secular equations. The degenerations in the spectrum can be interpreted as originating from an SU(2) symmetry of the dressed particles. The two particle scattering matrices obtained from the secular equations are consistent with this symmetry, and they differ in an overall sign in the two sectors.