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arXiv:hep-th/0610260 · Journal of Physics A Mathematical and Theoretical

Exactly solvable models of interacting spin-sparticles in one dimension

C.S. Melo, Marcio Jose Martins

Published Jan 9, 2007• 3 citations
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Abstract

We consider the eigenspectrum solution of a many-body problem of interacting spin- s particles that can be solvable within the generalized Bethe ansatz method. We assume that the interactions are encoded in terms of an arbitrary U (1) invariant factorizable S -matrix. The exact solution of the spin part is based on a unified formulation of the quantum inverse scattering method for an arbitrary (2 s + 1)-dimensional monodromy matrix. The respective eigenstates are shown to be given in terms of 2 s creation fields by a general new recurrence relation. This allows us to derive the spectrum and the respective Bethe ansatz equations.

DOI
10.1088/1751-8113/40/4/f03

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We consider the eigenspectrum solution of a many-body problem of interacting spin- s particles that can be solvable within the generalized Bethe ansatz method. We assume that the interactions are encoded in terms of an arbitrary U (1) invariant factorizable S -matrix. The exact solution of the spin part is based on a unified formulation of the quantum inverse scattering method for an arbitrary (2 s + 1)-dimensional monodromy matrix. The respective eigenstates are shown to be given in terms of 2 s creation fields by a general new recurrence relation. This allows us to derive the spectrum and the respective Bethe ansatz equations.
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We present the exact solution of a family of two-spins models. The models are solved by the algebraic Bethe ansatz method using the gl(2)gl(2)gl(2)-invariant RRR-matrix and a multi-spins Lax operator. The interactions are by the Heisenberg spins exchange. We are also considering magnetic BBB-fields and a term for Haldane single spin anisotropy.
The exact solution of the one-dimensional super-symmetric t-J model under generic integrable boundary conditions is obtained via the Bethe ansatz methods. With the coordinate Bethe ansatz, the corresponding R-matrix and K-matrices are derived for the second eigenvalue problem associated with spin degrees of freedom. It is found that the second eigenvalue problem can be transformed to that of the transfer matrix of the inhomogeneous XXX spin chain, which allows us to obtain the spectrum of the Hamiltonian and the associated Bethe ansatz equations by the off-diagonal Bethe ansatz method.
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