Real Space Renormalization Group Methods and Quantum Groups

TL;DR

This paper applies real-space renormalization group methods to quantum group invariant Hamiltonians, revealing how quantum group symmetry is preserved and analyzing critical lines and RG flow in the XXZ and Ising models.

Contribution

It demonstrates the application of real-space RG to quantum group invariant models, highlighting symmetry preservation and RG flow characteristics.

Findings

Correctly identifies the critical line of XXZ models.

RG flow in the Ising model matches tensor product decomposition of cyclic irreps.

Quantum group symmetry is preserved except for an anomalous term.

Abstract

We apply real-space RG methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field defined in an open chain with appropiate boundary terms. The quantum group symmetry is preserved under the RG transformation except for the appearence 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 irreps. of $SU_q(2)$ with $q^4=1$.