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Integrable mixing of An−1 type vertex models

Sergio Grillo, H. Montani

Given a family of monodromy matrices T0,T1,…,TK−1 corresponding to integrable anisotropic vertex models of Anμ−1 type, μ=0,1,…,K−1, we built up a related mixed vertex model by means of gluing the lattices on which they are defined, in such a way that integrability property is preserved. The gluing process is implemented through one-dimensional representations of rectangular quantum matrix algebras A(Rnμ−1:Rnμ), namely, the gluing matrices ζμ. Algebraic Bethe ansatz is applied on a pseudovacuum space with a selected basis and, for each element of this basis, it yields a set of nested Bethe ansatz equations matching up to the ones corresponding to an Am−1 quasiperiodic model, with m equal to minμ∈ZK{rank ζμ}.Given a family of monodromy matrices T0,T1,…,TK−1 corresponding to integrable anisotropic vertex models of Anμ−1 type, μ=0,1,…,K−1, we built up a related mixed vertex model by means of gluing the lattices on which they are defined, in such a way that integrability property is preserved. The gluing process is implemented through one-dimensional representations of rectangular quantum matrix algebras A(Rnμ−1:Rnμ), namely, the gluing matrices ζμ. Algebraic Bethe ansatz is applied on a pseudovacuum space with a selected basis and, for each element of this basis, it yields a set of nested Bethe ansatz equations matching up to the ones corresponding to an Am−1 quasiperiodic model, with m equal to minμ∈ZK{rank ζμ}.

arXiv:hep-ph/0206120Journal of Mathematical PhysicsApr 16, 20041 citation

The algebraic Bethe ansatz for rational braid-monoid lattice models

Marcio Jose Martins, P B Ramos

arXiv:hep-th/9703023Nuclear Physics BSep 1, 1997116 citations

Algebraic Bethe ansatz for an integrable Uq[Sl(n|m)] vertex model with mixed representations

G A P Ribeiro, Marcio Jose Martins

arXiv:nlin/0512035Nuclear Physics BJan 20, 20069 citations

Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries

Junpeng Cao, Wen‐Li Yang, Kangjie Shi +1 more

The nested off-diagonal Bethe ansatz method is proposed to diagonalize multi-component integrable models with generic integrable boundaries. As an example, the exact solutions of the su(n)-invariant spin chain model with both periodic and non-diagonal boundaries are derived by constructing the nested T − Q relations based on the operator product identities among the fused transfer matrices and the asymptotic behavior of the transfer matrices.

arXiv:1312.4770Journal of High Energy PhysicsApr 1, 201437 citations

Integrable vertex models and extended conformal invariance

Hector J. de Vega

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.

Journal of Physics A Mathematical and GeneralNov 21, 198834 citations

A new algebraic Bethe ansatz forgl(2,1) invariant vertex models

Markus P. Pfannmüller, Holger Frahm

The algebraic Bethe ansatz for the integrable vertex model constructed from the four-dimensional representation of the superalgebra gl(2,1) is calculated using a ferromagnetic reference state. This Bethe ansatz was known only for the three-dimensional representation leading to the supersymmetric t-J model. The necessary modification of the nested algebraic Bethe ansatz scheme and generalizations to related models are discussed.

Journal of Physics A Mathematical and GeneralAug 7, 199718 citations

Integrable mixed vertex models from braid-monoid algebra

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