Quantum Hamiltonians Generated by the R-Matrix of the Five-Vertex Model

We consider solutions of the RLL-relation with the R-matrix related to the five-vertex model. We show that in the case where the quantum space of the L-operator is infinite-dimensional and coincides with the Fock space of quantum oscillator, the solution of the RLL-relation gives a phase model with...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022-06, Vol.264 (3), p.271-285
Main Authors: Burenev, I. N., Pronko, A. G.
Format: Article
Language:English
Subjects:
Inhomogeneous systems
Mathematics
Mathematics and Statistics
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Summary:We consider solutions of the RLL-relation with the R-matrix related to the five-vertex model. We show that in the case where the quantum space of the L-operator is infinite-dimensional and coincides with the Fock space of quantum oscillator, the solution of the RLL-relation gives a phase model with two external fields. In the case of a two-dimensional quantum space, there exist two solutions each corresponding to the five-vertex model, and their special case, corresponding to the four-vertex model. We also derive explicit expressions for quantum Hamiltonians for the inhomogeneous systems in external fields, both in the finite- and infinite-dimensional cases.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05997-4