The $D^{(2)}_{3}$ spin chain and its finite-size spectrum

TL;DR

This paper studies the finite-size spectrum of the $D^{(2)}_{3}$ spin chain using the analytic Bethe ansatz, revealing its conformal field theory scaling behavior and identifying continuous and discrete states.

Contribution

It provides the first detailed analysis of the $D^{(2)}_{3}$ spin chain's scaling limit, including symmetry analysis and spectrum characterization.

Findings

Identification of effective scaling dimensions for a large class of states

Discovery of two compact and two continuous spectrum components

Conjecture on the central charge of the associated conformal field theory

Abstract

Using the analytic Bethe ansatz, we initiate a study of the scaling limit of the quasi-periodic $D^{(2)}_3$ spin chain. Supported by a detailed symmetry analysis, we determine the effective scaling dimensions of a large class of states in the parameter regime $\gamma\in (0,\frac{\pi}{4})$. Besides two compact degrees of freedom, we identify two independent continuous components in the finite-size spectrum. The influence of large twist angles on the latter reveals also the presence of discrete states. This allows for a conjecture on the central charge of the conformal field theory describing the scaling limit of the lattice model.