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Journal of Physics A Mathematical and General

Finite-size corrections for the low-lying states of the integrable model with two- and three-particle interactions

R. Z. Bariev

Published Mar 7, 1992• 19 citations
Publisher

Abstract

The finite-size corrections to the ground state and the energy of the low-lying states as a function of the size L are calculated for the one-dimensional integrable model with two- and three-particle interactions. It is shown that the conformal structure can be recovered if some extra conditions are imposed on the size and the ratio of the interaction parameters of the system. In this case the conformal properties of model are the same as those of the isotropic Heisenberg chain.

DOI
10.1088/0305-4470/25/5/010

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The finite-size corrections to the ground state and the energy of the low-lying states as a function of the size L are calculated for the one-dimensional integrable model with two- and three-particle interactions. It is shown that the conformal structure can be recovered if some extra conditions are imposed on the size and the ratio of the interaction parameters of the system. In this case the conformal properties of model are the same as those of the isotropic Heisenberg chain.
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The finite-size corrections to the ground state and the energy of the low magnetisation (S<<N) states as a function of the size N are calculated analytically for the one-dimensional half-filled Hubbard model with on-site repulsion (U>O). It is found that the contribution of the charge degrees of freedom is negligible, while the contribution of the spin degrees is the same as that in the one-dimensional isotropic Heisenberg model. The analytical results are compared to numerical ones obtained for the chain lengths up to N=512.
The methods of de Vega and Woynarovitch (1985) are used to calculate finite-size corrections to the ground state energy in different sectors for the XXZ Heisenberg chain, in the critical region -1< Delta <1. The finite-size scaling amplitude for the mass gap between the lowest lying sectors is derived. Using conformal invariance, the scaling dimension is extracted for an associated operator, corresponding to the electric field operator in the 8-vertex model. The conjecture of Baxter and Kelland (1974) for the electric field exponent is confirmed.