Integrable three-state vertex models with weights lying on genus five curves

Abstract

We investigate the Yang-Baxter algebra for $\mathrm{U}(1)$ invariant three-state vertex models whose Boltzmann weights configurations break explicitly the parity-time reversal symmetry. We uncover two families of regular Lax operators with nineteen non-null weights which ultimately sit on algebraic plane curves with genus five. We argue that these curves admit degree two morphisms onto elliptic curves and thus they are bielliptic. The associated $\mathrm{R}$-matrices are non-additive in the spectral parameters and it has been checked that they satisfy the Yang-Baxter equation. The respective integrable quantum spin-1 Hamiltonians are exhibited.

53 pages

References in corpus (2)

• The Yang-Baxter equation for PT invariant nineteen vertex models
• Algebraic Bethe Ansatz for U(1) Invariant Integrable Models: The Method and General Results

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• 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