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arXiv · hep-th/9511190

The Renormalization Group Method and Quantum Groups: the postman always rings twice

Miguel A. Martin-Delgado·German Sierra
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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 $SU_q(2)$ with $q^4=1$.

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Miguel A. Martin-Delgado, German Sierra. 1995-11-27. The Renormalization Group Method and Quantum Groups: the postman always rings twice. https://doi.org/10.1142/9789812830425_0007

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