Classification of three-state Hamiltonians solvable by the coordinate Bethe ansatz

We classify 'all' Hamiltonians with rank 1 symmetry and nearest-neighbour interactions, acting on a periodic three-state spin chain, and solvable through (generalization of) the coordinate Bethe ansatz (CBA). In this way we obtain four multi-parametric extensions of the known 19-vertex Ham...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2013-10, Vol.46 (40), p.405001-27
Main Authors: Crampé, N, Frappat, L, Ragoucy, E
Format: Article
Language:English
Subjects:
Chains
Classification
Eigenfunctions
High Energy Physics - Theory
Mathematical analysis
Mathematical Physics
Mathematics
Physics
Specifications
Symmetry
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Summary:We classify 'all' Hamiltonians with rank 1 symmetry and nearest-neighbour interactions, acting on a periodic three-state spin chain, and solvable through (generalization of) the coordinate Bethe ansatz (CBA). In this way we obtain four multi-parametric extensions of the known 19-vertex Hamiltonians (such as Zamolodchikov-Fateev, Izergin-Korepin and Bariev Hamiltonians). Apart from the 19-vertex Hamiltonians, there exist 17-vertex and 14-vertex Hamiltonians that cannot be viewed as subcases of the 19-vertex ones. In the case of 17-vertex Hamiltonians, we get a generalization of the genus 5 special branch found by Martins, plus three new ones. We also get two 14-vertex Hamiltonians. We solve all these Hamiltonians using CBA, and provide their spectrum, eigenfunctions and Bethe equations. Special attention is given to provide the specifications of our multi-parametric Hamiltonians that give back known Hamiltonians.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/46/40/405001