The matrix product ansatz for the six-vertex model

Matheus J. Lazo

Physica A: Statistical Mechanics and its Applications, 2007, vol. 374, issue 2, 655-662

Abstract: Recently it was shown that the eigenfunctions for the asymmetric exclusion problem and several of its generalizations as well as a huge family of quantum chains, like the anisotropic Heisenberg model, Fateev–Zamolodchikov model, Izergin–Korepin model, Sutherland model, t–J model, Hubbard model, etc, can be expressed by a matrix product ansatz. Differently from the coordinate Bethe ansatz, where the eigenvalues and eigenvectors are plane wave combinations, in this ansatz the components of the eigenfunctions are obtained through the algebraic properties of properly defined matrices. In this work, we introduce a formulation of a matrix product ansatz for the six-vertex model with periodic boundary condition, which is the paradigmatic example of integrability in two dimensions. Remarkably, our studies of the six-vertex model are in agreement with the conjecture that all models exactly solved by the Bethe ansatz can also be solved by an appropriated matrix product ansatz.

Keywords: Matrix product ansatz; Bethe ansatz; Vertex models (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:374:y:2007:i:2:p:655-662

DOI: 10.1016/j.physa.2006.08.001

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