Real space renormalization group methods and quantum groups.

Abstract

We apply real space renormalization group (RG) methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field (ITF) defined in an open chain with appropriate boundary terms. The quantum group symmetry is preserved under the RG transformation except for the appearance of a quantum group anomalous term which vanishes in the classical case. We obtain correctly the line of critical XXZ models. In the ITF model the RG flow coincides with the tensor product decomposition of cyclic irreducible representations of ${\mathrm{SU}}_{q}\left(2\right)$ with ${q}^{4}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$.