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

Abstract

We consider the $U_q[SU(2)]$ symmetric Heisenberg chain when $q=e^{iπ/(m+1)}$ 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)