The complete conformal spectrum of a $sl(2|1)$ invariant network model and logarithmic corrections

TL;DR

This paper analyzes the low-temperature and finite-size spectra of Temperley-Lieb models, focusing on logarithmic corrections and the complete conformal spectrum of an $sl(2|1)$ invariant network model, revealing large degeneracies.

Contribution

It provides the full set of scaling dimensions for the $sl(2|1)$ invariant 3-state Temperley-Lieb model at $ ext{Delta}=1/2$, highlighting degeneracies and logarithmic corrections.

Findings

Logarithmic corrections appear in susceptibility and spectrum at $ ext{Delta}=1/2$

Complete conformal spectrum with large degeneracies is determined

Degeneracies are linked to the $sl(2|1)$ symmetry

Abstract

We investigate the low temperature asymptotics and the finite size spectrum of a class of Temperley-Lieb models. As reference system we use the spin-1/2 Heisenberg chain with anisotropy parameter $\Delta$ and twisted boundary conditions. Special emphasis is placed on the study of logarithmic corrections appearing in the case of $\Delta=1/2$ in the bulk susceptibility data and in the low-energy spectrum yielding the conformal dimensions. For the $sl(2|1)$ invariant 3-state representation of the Temperley-Lieb algebra with $\Delta=1/2$ we give the complete set of scaling dimensions which show huge degeneracies.