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arXiv:1909.07434

The exact solution of a generalized two-spins model

Santos, G.

Published Sep 16, 2019• 0 citations
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Abstract

We present the exact solution of a family of two-spins models. The models are solved by the algebraic Bethe ansatz method using the $gl(2)$-invariant $R$-matrix and a multi-spins Lax operator. The interactions are by the Heisenberg spins exchange. We are also considering magnetic $B$-fields and a term for Haldane single spin anisotropy.

DOI
10.48550/arxiv.1909.07434

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I introduce a new parametrization of a bosonic Lax operator for the algebraic Bethe ansatz method with the gl(2)gl(2)gl(2)-invariant RRR-matrix and use it to present the exact solution of a generalized two-sites Bose-Hubbard model with asymmetric tunnelling. In the no interaction limit I show that the Bethe ansatz equations can be written as a SN−1S^{N-1}SN−1 sphere, where NNN is the total number of atoms in the condensate.
I study the technique of Algebraic Bethe Ansatz for solving integrable models and show how it works in detail on the simplest example of spin 1/2 XXX magnetic chain. Several other models are treated more superficially, only the specific details are given. Several parameters, appearing in these generalizations: spin sss, anisotropy parameter $\ga$, shift $\om$ in the alternating chain, allow to include in our treatment most known examples of soliton theory, including relativistic model of Quantum Field Theory.
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