Finite size spectrum of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$-invariant boundary conditions

TL;DR

This paper investigates the finite size spectrum of a critical staggered XXZ spin chain with quantum group invariant boundaries, revealing continuous and discrete spectral components linked to a non-compact conformal field theory.

Contribution

It demonstrates the presence of a continuous spectrum component and discrete levels in the finite size spectrum of the model, extending understanding of its conformal field theory description.

Findings

Spectrum includes continuous and discrete components.

Finite size amplitudes relate to eigenvalues of a quasi-momentum operator.

Spectrum behavior varies with the staggering parameter.

Abstract

The finite size spectrum of the critical $\mathbb{Z}_2$-staggered spin-$1/2$ XXZ model with quantum group invariant boundary conditions is studied. For a particular (self-dual) choice of the staggering the spectrum of conformal weights of this model has been recently been shown to have a continuous component, similar as in the model with periodic boundary conditions whose continuum limit has been found to be described in terms of the non-compact $SU(2,\mathbb{R})/U(1)$ Euclidean black hole conformal field theory (CFT). Here we show that the same is true for a range of the staggering parameter. In addition we find that levels from the discrete part of the spectrum of this CFT emerge as the anisotropy is varied. The finite size amplitudes of both the continuous and the discrete levels are related to the corresponding eigenvalues of a quasi-momentum operator which commutes with the Hamiltonian and the transfer matrix of the model.