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Journal of Physics A Mathematical and General

Conformal invariance and finite one-dimensional quantum chains

G von Gehlen, V. Rittenberg, H. Ruegg

Published Jan 11, 1986• 117 citations
Publisher

Abstract

Based on previous work of Cardy (1984), the authors show in a systematic way how using conformal invariance one can determine the anomalous dimensions of various operators from finite quantum chains with different boundary conditions. The method is illustrated in the case of the three- and four-state Potts models where the anomalous dimensions of the para-fermionic operators are found.

DOI
10.1088/0305-4470/19/1/014

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Based on previous work of Cardy (1984), the authors show in a systematic way how using conformal invariance one can determine the anomalous dimensions of various operators from finite quantum chains with different boundary conditions. The method is illustrated in the case of the three- and four-state Potts models where the anomalous dimensions of the para-fermionic operators are found.
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A quantum spin model with three-spin coupling is studied by finite-lattice methods. The critical indices nu and alpha are obtained by standard finite-size scaling analysis. Conformal invariance is used to estimate the exponents nu and eta , the central charge or conformal anomaly c and the anomalous dimension of a spin 1/4 parafermion. The authors conclude that the model belongs to the same universality class as the four-state Potts and Baxter-Wu models, although the convergence of the various finite lattice estimators is extremely slow.
The authors study the finite-size effects for the fourth-state one-dimensional quantum chain introduced by Kohmoto et al. (1981) using different boundary conditions. From the corrections to the ground-state energy for periodic boundary conditions they verify that the central charge of the Virasoro algebra is equal to one in the whole domain of criticality. Their numerical study suggests a new relation between the corrections to the ground-state energy with free boundary conditions and with periodic boundary conditions. Various critical exponents including the surface ones and those corresponding to the para-fermions are determined.
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