Diagrammatic evaluation of conformal weights in the U_q[SU(2)] symmetric Heisenberg chain

TL;DR

This paper uses diagrammatic techniques to analyze the finite size scaling of ground states in the $U_q[SU(2)]$ symmetric Heisenberg chain at specific roots of unity, confirming predictions for the Ising and 3-state Potts models.

Contribution

It introduces a diagrammatic method based on Temperley-Lieb algebra to compute levels and analyze finite size scaling in $U_q[SU(2)]$ symmetric chains at roots of unity.

Findings

Results match finite size scaling predictions for Bethe levels.

Diagrammatic technique simplifies computation of levels.

Analysis covers Ising and 3-state Potts models.

Abstract

We consider the $U_q[SU(2)]$ symmetric Heisenberg chain when $q=e^{i\pi/(m+1)}$ and $m$ is integer. We consider the cases $m=3$ and $m=5$ which correspond to the Ising and 3-state Potts models. We study the finite size scaling (FSS) of the ground states in different quantum spin sectors and restricting to highest weights of type-II representations. We compute the levels by a diagrammatic technique which needs only the commutation relations of the underlying Temperley-Lieb algebra. The results match the FSS predictions which hold for the Bethe levels. (2 PostScript figures (or the corresponding tables) available from the author)