# On the critical behaviour of the integrable $q$-deformed $OSp(3|2)$ superspin chain

## TL;DR

This paper investigates the critical behavior of an integrable $q$-deformed $OSp(3|2)$ superspin chain, revealing complex finite-size effects, composite critical exponents, and rich spectral structures through Bethe ansatz analysis.

## Contribution

It provides a detailed analysis of the finite-size spectra and critical exponents of the $q$-deformed $OSp(3|2)$ superspin chain, highlighting novel composite structures and degeneracy lifting mechanisms.

## Key findings

- Critical exponents are composed of Coulomb gas dimensions and $Z(2)$ degrees.
- Spectrum contains $S=1$ XXZ chain features at specific deformation.
- Finite-size effects include logarithmic corrections and power-law behaviors.

## Abstract

This paper is concerned with the investigation of the massless regime of an integrable spin chain based on the quantum group deformation of the $OSp(3|2)$ superalgebra. The finite-size properties of the eigenspectra are computed by solving the respective Bethe ansatz equations for large system sizes allowing us to uncover the low-lying critical exponents. We present evidences that critical exponents appear to be built in terms of composites of anomalous dimensions of two Coulomb gases with distinct radii and the exponents associated to $Z(2)$ degrees of freedom. This view is supported by the fact that the $S=1$ XXZ integrable chain spectrum is present in some of the sectors of our superspin chain at a particular value of the deformation parameter. We find that the fine structure of finite-size effects is very rich for a typical anisotropic spin chain. In fact, we argue on the existence of a family of states with the same conformal dimension whose lattice degeneracies are apparently lifted by logarithmic corrections. On the other hand we also report on states of the spectrum whose finite-size corrections seem to be governed by a power law behaviour. We finally observe that under toroidal boundary conditions the ground state dependence on the twist angle has two distinct analytical structures.