arXiv:nlin/0512063

Integrable Vertex Models with General Twists

Marcio Jose Martins

Published Dec 21, 2005• 0 citations

Abstract

DOI: 10.48550/arxiv.nlin/0512063

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arXiv:nlin/0512063

Integrable Vertex Models with General Twists

Marcio Jose Martins

Published Dec 21, 2005• 0 citations

arXiv HTML PDF

Abstract

B_n

D_n

and

C_n

Lie algebras are presented. The applicability of this approach to the eight vertex model with non-diagonal twists is also discussed.

DOI: 10.48550/arxiv.nlin/0512063

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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 $B_{n},$ $D_{n}$ and $C_{n}$ Lie algebras are presented.The applicability of this approach to the eight vertex model with non-diagonal twists is also discussed.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 $B_{n},$ $D_{n}$ and $C_{n}$ Lie algebras are presented.The applicability of this approach to the eight vertex model with non-diagonal twists is also discussed.

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Abstract We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted ${D}_3^{(2)}$ D 3 2 algebra (or the ${D}_3^{(2)}$ D 3 2 model) with either periodic or integrable open boundary conditions. We obtain the intrinsic operator product identities among the fused transfer matrices and find a way to close the recursive fusion relations, which makes it possible to determinate eigenvalues of transfer matrices with an arbitrary anisotropic parameter η. Based on them, and the asymptotic behaviors and values at certain points, we construct eigenvalues of transfer matrices in terms of homogeneous T − Q relations for the periodic case and inhomogeneous ones for the open case with some off-diagonal boundary reflections. The associated Bethe ansatz equations are also given. The method and results in this paper can be generalized to the ${D}_{n+1}^{(2)}$ D n + 1 2 model and other high rank integrable models.Abstract We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted $$ {D}_3^{(2)} $$ D 3 2 algebra (or the $$ {D}_3^{(2)} $$ D 3 2 model) with either periodic or integrable open boundary conditions. We obtain the intrinsic operator product identities among the fused transfer matrices and find a way to close the recursive fusion relations, which makes it possible to determinate eigenvalues of transfer matrices with an arbitrary anisotropic parameter η. Based on them, and the asymptotic behaviors and values at certain points, we construct eigenvalues of transfer matrices in terms of homogeneous T − Q relations for the periodic case and inhomogeneous ones for the open case with some off-diagonal boundary reflections. The associated Bethe ansatz equations are also given. The method and results in this paper can be generalized to the $$ {D}_{n+1}^{(2)} $$ D n + 1 2 model and other high rank integrable models.

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Sep 3, 199380 citations

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Rodrigo A. Pimenta, A. Lima-Santos

arXiv:1406.5757Journal of Statistical Mechanics Theory and ExperimentNov 6, 20142 citations

B_n

D_n

and

C_n

Lie algebras are presented. The applicability of this approach to the eight vertex model with non-diagonal twists is also discussed.

B_{n},

D_{n}

and

C_{n}

Lie algebras are presented.The applicability of this approach to the eight vertex model with non-diagonal twists is also discussed.

Exact solution of the quantum integrable model associated with the twisted

{\mathrm{D}}_3^{(2)}

algebra

Abstract We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted

{D}_3^{(2)}

D 3 2 algebra (or the

{D}_3^{(2)}

D 3 2 model) with either periodic or integrable open boundary conditions. We obtain the intrinsic operator product identities among the fused transfer matrices and find a way to close the recursive fusion relations, which makes it possible to determinate eigenvalues of transfer matrices with an arbitrary anisotropic parameter η. Based on them, and the asymptotic behaviors and values at certain points, we construct eigenvalues of transfer matrices in terms of homogeneous T − Q relations for the periodic case and inhomogeneous ones for the open case with some off-diagonal boundary reflections. The associated Bethe ansatz equations are also given. The method and results in this paper can be generalized to the

{D}_{n+1}^{(2)}

D n + 1 2 model and other high rank integrable models.

Exact solution of the

SU_{q}(n)

invariant quantum spin chains

The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the

A_{n-1}

vertex model with fixed open boundary conditions and the corresponding

SU_{q}(n)

invariant hamiltonian. The Bethe Ansatz equations obtained are solved in the thermodynamic limit giving the vertex model free energy and the hamiltonian ground state energy including the corresponding boundary contributions.