Excited states in the twisted XXZ spin chain

TL;DR

This paper analyzes the finite size spectrum of the twisted XXZ spin chain using Bethe Ansatz and string hypothesis, revealing connections to conformal field theory and primary states in the Kac table.

Contribution

It introduces a coupled non-linear integral equation approach for solving Bethe Ansatz equations in the twisted XXZ chain, extending understanding of its spectrum and conformal field theory correspondence.

Findings

Spectrum computed for various twists and anisotropies.

Connection established between the model and unitary conformal field theory.

All primary states in the Kac table are recovered.

Abstract

We compute the finite size spectrum for the spin 1/2 XXZ chain with twisted boundary conditions, for anisotropy in the regime $0< \gamma <\pi/2$, and arbitrary twist $\theta$. The string hypothesis is employed for treating complex excitations. The Bethe Ansatz equtions are solved within a coupled non-linear integral equation approach, with one equation for each type of string. The root-of-unity quantum group invariant periodic chain reduces to the XXZ_1/2 chain with a set of twist boundary conditions ($\pi/\gamma\in Z$, $\theta$ an integer multiple of $\gamma$). For this model, the restricted Hilbert space corresponds to an unitary conformal field theory, and we recover all primary states in the Kac table in terms of states with specific twist and strings.