Classification of three-state Hamiltonians solvable by Coordinate Bethe Ansatz

Abstract

We classify all Hamiltonians with rank 1 symmetry, acting on a periodic three-state spin chain, and solvable through (generalisation of) the coordinate Bethe ansatz (CBA). We obtain in this way four multi-parametric extensions of the known 19-vertex Hamiltonians (such as Zamolodchikov-Fateev, Izergin-Korepin, Bariev Hamiltonians). Apart from the 19-vertex Hamiltonians, there exists 17-vertex and 14-vertex Hamiltonians that cannot be viewed as subcases of the 19-vertex ones. In the case of 17-vertex Hamiltonian, we get a generalization of the genus 5 special branch found by Martins, plus three new ones. We get also two 14-vertex Hamiltonians. We solve all these Hamiltonians using CBA, and provide their spectrum, eigenfunctions and Bethe equations. A special attention is made to provide the specifications of our multi-parametric Hamiltonians that give back known Hamiltonians.

30 pages; web page: http://www.coulomb.univ-montp2.fr/3Ham

References in corpus (10)

• Degenerate Fermi Gases of Ytterbium
• All-Optical Formation of Quantum Degenerate Mixtures
• Bose-Einstein Condensation of an Ytterbium Isotope
• Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
• Matrix Coordinate Bethe Ansatz: Applications to XXZ and ASEP models
• Generalized coordinate Bethe ansatz for non diagonal boundaries
• Integrable three-state vertex models with weights lying on genus five curves
• Coordinate Bethe Ansatz for Spin s XXX Model
• Phase diagram and spectral properties of a new exactly integrable spin one quantum chain
• Bethe ansatz for the Temperley-Lieb spin-chain with integrable open boundaries

Cited by in corpus (8)

• Yang-Baxter and the Boost: splitting the difference
• Onsager symmetries in $U(1)$-invariant clock models
• R-matrices of three-state Hamiltonians solvable by Coordinate Bethe Ansatz
• 3-state Hamiltonians associated to solvable 33-vertex models
• An Integrable Nineteen Vertex Model Lying on a Hypersurface
• Integrable models on Rydberg atom chains
• Reflection $K$-matrices for a nineteen vertex model with $U_q[\mathrm{osp}{\left(2|2\right)}^{\left(2\right)}]$ symmetry
• The spectrum of a vertex model and related spin one chain sitting in a genus five curve