The Renormalization Group Method and Quantum Groups: the postman always rings twice
arXiv:hep-th/9511190 · doi:10.1142/9789812830425_0007
Abstract
We review some of our recent results concerning the relationship between the Real-Space Renormalization Group method and Quantum Groups. We show this relation by applying real-space 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 appearence of a quantum group anomalous term which vanishes in the classical case. This is called {\em the quantum group anomaly}. We derive the new qRG equations for the XXZ model and show that the RG-flow diagram obtained in this fashion exhibits the correct line of critical points that the exact model has. In the ITF model the qRG-flow equations coincide with the tensor product decomposition of cyclic irreps of with .
LATEX file, 21 pages, no figures. To appear in "From Field Theory to Quantum Groups", World Scientific. Proceedings to honor J.Lukierski in his 60th birthday