https://doi.org/10.1140/epjp/s13360-023-04711-w
Regular Article
Integrability in ![$$[d+1]$$](/articles/epjplus/abs/2023/11/13360_2023_Article_4711/13360_2023_Article_4711_tex_eq1.png)
dimensions: combined local equations and commutativity of the transfer matrices
A. I. Alikhanyan National Science Laboratory (YerPhI), Alikhanian Br. str. 2, 36, Yerevan, Armenia
Received:
30
September
2023
Accepted:
20
November
2023
Published online:
30
November
2023
We propose new inhomogeneous local integrability equations–combined equations, for statistical vertex models of general dimensions in the framework of the Algebraic Bethe Ansatz (ABA). For the low-dimensional cases the efficiency of the step-by-step consideration of the transfer matrices’ commutation is demonstrated. We construct some simple 3D solutions with the three-state R-matrices of certain 20-vertex structure; the connection with the quantum three-qubit gates is discussed. New, restricted versions of 3D local integrability equations with four-state R-matrices are defined, too. Then we construct a new 3D analog of the two-dimensional star-triangle equations.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
