3-state Hamiltonians associated to solvable 33-vertex models

Using the nested coordinate Bethe ansatz, we study 3-state Hamiltonians with 33 non-vanishing entries, or 33-vertex models, where only one global charge with degenerate eigenvalues exists and each site possesses three internal degrees of freedom. In the context of Markovian processes, they correspon...

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Bibliographic Details
Published in:Journal of mathematical physics 2016-09, Vol.57 (9), p.1
Main Authors: Crampé, N., Frappat, L., Ragoucy, E., Vanicat, M.
Format: Article
Language:English
Subjects:
Constraint modelling
Diffusion
Eigenvalues
Markov analysis
Markov processes
Mathematical Physics
Mathematics
Physics
Statistics
Transmutation
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Summary:Using the nested coordinate Bethe ansatz, we study 3-state Hamiltonians with 33 non-vanishing entries, or 33-vertex models, where only one global charge with degenerate eigenvalues exists and each site possesses three internal degrees of freedom. In the context of Markovian processes, they correspond to diffusing particles with two possible internal states which may be exchanged during the diffusion (transmutation). The first step of the nested coordinate Bethe ansatz is performed providing the eigenvalues in terms of rapidities. We give the constraints ensuring the consistency of the computations. These rapidities also satisfy Bethe equations involving 4 × 4 R-matrices, solutions of the Yang–Baxter equation which implies new constraints on the models. We solve them allowing us to list all the solvable 33-vertex models.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4962920