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The Eight Vertex Model. New results

K. Fabricius, Barry M. McCoy

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

Whereas the tools to determine the eigenvalues of the eight-vertex transfer matrix T are well known there has been until recently incomplete knowledge about the eigenvectors of T. We describe the construction of eigenvectors of T corresponding to degenerate eigenvalues and discuss the related hidden elliptic symmetry.

Related papers

The Eight Vertex Model.New results

K. Fabricius, Barry M. McCoy

Whereas the tools to determine the eigenvalues of the eight-vertex transfer matrix T are well known there has been until recently incomplete knowledge about the eigenvectors of T. We describe the construction of eigenvectors of T corresponding to degenerate eigenvalues and discuss the related hidden elliptic symmetry.

arXiv:cond-mat/0612699•Dec 29, 2006•0 citations

An Elliptic Current Operator for the Eight Vertex Model

K. Fabricius

Whereas the tools to determine the eigenvalues of the eight-vertex transfer matrix T are well known there has been until recently incomplete knowledge about the eigenvectors of T. We describe the construction of eigenvectors of T corresponding to degenerate eigenvalues and discuss the related hidden elliptic symmetry.

•Aug 8, 2007•5 citations

An elliptic current operator for the eight-vertex model

Klaus Fabricius, Barry M. McCoy

We compute the operator which creates the missing degenerate states in the algebraic Bethe ansatz of the eight-vertex model at roots of unity and relate it to the concept of an elliptic current operator. We find that in sharp contrast with the corresponding formalism in the six-vertex model at roots of unity [12] the current operator is not nilpotent with the consequence that in the construction of degenerate eigenstates of the transfer matrix an arbitrary number of exact strings can be added to the set of regular Bethe roots. Thus the original set of free parameters { s , t } of an eigenvector of the transfer matrix T is enlarged to become { s , t , λ c ,1 , ..., λ c , n } with arbitrary string centres λ c , j and arbitrary n .

arXiv:cond-mat/0606190•Journal of Physics A Mathematical and General•Nov 15, 2006•16 citations

Eight-Vertex Model in Lattice Statistics and One-Dimensional Anisotropic Heisenberg Chain: III. Eigenvectors of the Transfer Matrix and Hamiltonian

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Abstract We obtain the eigenvectors of the transfer matrix of the zero-field eight vertex model. These are also the eigenvectors of the Hamiltonian of the corresponding one-dimensional anistropic Heisenberg chain.

Advanced series in mathematical physics•Mar 1, 1990•2 citations

Eight-vertex model in lattice statistics and one-dimensional anisotropic heisenberg chain. III. Eigenvectors of the transfer matrix and hamiltonian

R. J. Baxter

Annals of Physics•Mar 1, 1973•199 citations

Eight-Vertex Model in Lattice Statistics and One-Dimensional Anisotropic Heisenberg Chain: I. Some Fundamental Eigenvectors

R. J. Baxter

Abstract We obtain some simple eigenvectors of the transfer matrix of the zero-field eight-vertex model. These are also eigenvectors of the Hamiltonian of the one-dimensional anisotropic Heisenberg chain. We also obtain new equations for the matrix Q ( v ) introduced in earlier papers.

Advanced series in mathematical physics•Mar 1, 1990•1 citation
We compute the operator which creates the missing degenerate states in the algebraic Bethe ansatz of the eight-vertex model at roots of unity and relate it to the concept of an elliptic current operator. We find that in sharp contrast with the corresponding formalism in the six-vertex model at roots of unity [12] the current operator is not nilpotent with the consequence that in the construction of degenerate eigenstates of the transfer matrix an arbitrary number of exact strings can be added to the set of regular Bethe roots. Thus the original set of free parameters { s , t } of an eigenvector of the transfer matrix T is enlarged to become { s , t , λ c ,1 , ..., λ c , n } with arbitrary string centres λ c , j and arbitrary n .