Bethe Ansatze for 19-vertex Models

Abstract

The nineteen-vertex models of Zamolodchikov-Fateev, Izergin-Korepin and the supersymmetric osp(1|2) with periodic boundary conditions are studied. We find the spectrum of these quantum spin chains using the Coordinate Bethe Ansatz. The approche is a suitable parametrization of their wavefunctions. We also applied the Algebraic Bethe Ansatz in order to obtain the eigenvalues and eigenvectors of the corresponding transfer matrices.

30 pages, Latex, references added, no signficant changes

References in corpus (6)

• The algebraic Bethe ansatz for rational braid-monoid lattice models
• Off-Shell Bethe Ansatz Equation for Gaudin Magnets and Solutions of Knizhnik-Zamolodchikov Equations
• Integrable vertex and loop models on the square lattice with open boundaries via reflection matrices
• Edge States in Strong Magnetic Field
• The exact solution and the finite size behaviour of the $Osp(1|2)$ invariant spin chain
• Exact solution of the deformed biquadratic spin 1 hamiltonian

Cited by in corpus (16)

• Trigonometric osp(1|2) Gaudin model
• Algebraic Bethe Ansatz for the Zamolodchikov-Fateev and Izergin-Korepin models with open boundary conditions
• Off-Shell Bethe Ansatz Equation for $osp(2|1)$ Gaudin Magnets
• Higher spin vertex models with domain wall boundary conditions
• R-matrices of three-state Hamiltonians solvable by Coordinate Bethe Ansatz
• Classification of three-state Hamiltonians solvable by Coordinate Bethe Ansatz
• $sl(2|1{)}^{(2)}$ Gaudin Magnet and its associated Knizhnik-Zamolodchikov equation
• Coordinate Bethe Ansatz for Spin s XXX Model
• Coupled Fredkin and Motzkin chains from quantum six- and nineteen-vertex models
• OPE in planar QCD from integrability
• $A_2^{(2)}$ Gaudin model and its associated Knizhnik-Zamolodchikov equation
• Reflection $K$-matrices for a nineteen vertex model with $U_q[\mathrm{osp}{\left(2|2\right)}^{\left(2\right)}]$ symmetry
• On the algebraic Bethe ansatz: Periodic boundary conditions
• A tale of two Bethe ansätze
• Spin-$s$ $U(1)$-eigenstate preparation
• Boundary Algebraic Bethe Ansatz for a nineteen vertex model with $U_q[\mathrm{osp}(2|2{)}^{(2)}]$ symmetry