Integrability in [d+1] dimensions: combined local equations and commutativity of the transfer matrices
- Resource Type
- Original Paper
- Authors
- Khachatryan, Shahane A.
- Source
- The European Physical Journal Plus. 138(11)
- Subject
- Language
- English
- ISSN
- 2190-5444
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.