Finite-size effects in the spectrum of the $OSp(3|2)$ superspin chain

TL;DR

This paper investigates the finite-size effects in the spectrum of an $OSp(3|2)$ superspin chain, revealing a continuous spectrum and logarithmic decay of watermelon correlation functions, advancing understanding of critical properties in integrable models.

Contribution

It provides the first detailed finite-size analysis of the $OSp(3|2)$ superspin chain, demonstrating the existence of a continuum of scaling dimensions and conjecturing logarithmic decay of correlation functions.

Findings

Existence of continua of scaling dimensions starting at the ground state.

Logarithmic decay of watermelon correlation functions with exponents related to the quadratic Casimir.

The continuous spectrum persists regardless of boundary condition changes.

Abstract

The low energy spectrum of a spin chain with $OSp(3|2)$ supergroup symmetry is studied based on the Bethe ansatz solution of the related vertex model. This model is a lattice realization of intersecting loops in two dimensions with loop fugacity $z=1$ which provides a framework to study the critical properties of the unusual low temperature Goldstone phase of the $O(N)$ sigma model for $N=1$ in the context of an integrable model. Our finite-size analysis provides strong evidence for the existence of continua of scaling dimensions, the lowest of them starting at the ground state. Based on our data we conjecture that the so-called watermelon correlation functions decay logarithmically with exponents related to the quadratic Casimir operator of $OSp(3|2)$. The presence of a continuous spectrum is not affected by a change to the boundary conditions although the density of states in the continua appears to be modified.