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Journal of Physics A Mathematical and General

Operator content of the Blume-Capel quantum chain

Deborah Brasil Balbao, J. R. Drugowich de Felício

Published Mar 11, 1987• 26 citations
Publisher

Abstract

The authors calculated the conformal anomaly number of the Blume-Capel quantum chain via finite-size corrections to the ground-state energy. In addition they compute, at the tricritical point, the lowest excitations of the spectrum to be compared with the theoretical description in terms of the irreducible representations of the corresponding Virasoro algebra.

DOI
10.1088/0305-4470/20/4/005

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The authors calculated the conformal anomaly number of the Blume-Capel quantum chain via finite-size corrections to the ground-state energy. In addition they compute, at the tricritical point, the lowest excitations of the spectrum to be compared with the theoretical description in terms of the irreducible representations of the corresponding Virasoro algebra.
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We show that the recently developed pseudoparticle-operator algebra which generates the low-energy Hamiltonian eigenstates of multicomponent integrable systems with contact interactions also provides a natural operator representation for the Virasoro algebras associated with the conformal-invariant character of the low-energy spectrum of these models. Studying explicitly the Hubbard chain in a nonzero chemical potential and external magnetic field, we establish that the pseudoparticle-perturbation theory provides a correct starting point for the construction of a suitable critical-point Hamiltonian. We derive explicit expressions in terms of pseudoparticle operators for the generators of the Virasoro algebras and the energy-momentum tensor, describe the conformal-invariant character of the critical point from the point of view of the response to curvature of the two-dimensional space time, and discuss the relation to Kac-Moody algebras and dynamical separation.