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Journal of Physics A Mathematical and General

Integrable vertex models and extended conformal invariance

Hector J. de Vega

Published Nov 21, 1988• 34 citations
Publisher

Abstract

Transfer matrix eigenvalues are exactly computed for large but finite size for a general class of q-state vertex models (q different states per bond, 2<or=q) from their nested Bethe ansatz equations. The conformal dimensions here obtained vary continuously as functions of the anisotropy parameter and express nicely in terms of the Cartan matrix of the underlying Lie algebra. They indicate the presence of an extended conformal invariance.

DOI
10.1088/0305-4470/21/22/009

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Transfer matrix eigenvalues are exactly computed for large but finite size for a general class of q-state vertex models (q different states per bond, 2<or=q) from their nested Bethe ansatz equations. The conformal dimensions here obtained vary continuously as functions of the anisotropy parameter and express nicely in terms of the Cartan matrix of the underlying Lie algebra. They indicate the presence of an extended conformal invariance.
The fused six-vertex models with open boundary conditions are studied. The Bethe ansatz solution given by Sklyanin has been generalized to the transfer matrices of the fused models. We have shown that the eigenvalues of transfer matrices satisfy a group of functional relations, which are the su(2) fusion rule held by the transfer matrices of the fused models. The fused transfer matrices form a commuting family and also commute with the quantum group Uq[sl(2)]. In the case of the parameter qh = −1 (h = 4,5, · · ·) the functional relations in the limit of spectral parameter u → i ∞ are truncated. This shows that the su(2) fusion rule with finite level appears for the six vertex model with the open boundary conditions. We have solved the functional relations to obtain the finite-size corrections of the fused transfer matrices for low-lying excitations. From the corrections the central charges and conformal weights of underlying conformal field theory are extracted. To see different boundary conditions we also have studied the six-vertex model with a twisted boundary condition. hep-th/9502053; to appear in NPB. 1
We review recent progress towards the solution of exactly solved isotropic vertex models with arbitrary toroidal boundary conditions.Quantum space transformations make it possible the diagonalization of the corresponding transfer matrices by means of the quantum inverse scattering method.Explicit expressions for the eigenvalues and Bethe ansatz equations of the twisted isotropic spin chains based on the Bn,B_{n},Bn​, DnD_{n}Dn​ and CnC_{n}Cn​ Lie algebras are presented.The applicability of this approach to the eight vertex model with non-diagonal twists is also discussed.