Simplified tetrahedron equations: Fermionic realization

Abstract

The natural generalization of the (two-dimensional) Yang-Baxter equations to three dimensions is known as the Zamolodchikov's tetrahedron equations. We consider a simplified version of these equations which still ensures the commutativity of the transfer matrices with different spectral parameters and we present a family of free fermionic solutions.

Latex file, 24 pages, 4 figures

References in corpus (5)

• Star-Triangle Relation for a Three Dimensional Model
• Edge Excitations of an Incompressible Fermionic Liquid in a Disorder Magnetic Field
• Elliptic solution for modified tetrahedron equations
• Explicit Free Parameterization of the Modified Tetrahedron Equation
• An Integrable Model with non-reducible three particle R-Matrix

Cited by in corpus (3)

• On the solutions of the Yang-Baxter equations with general inhomogeneous eight-vertex $R$-matrix: Relations with Zamolodchikov's tetrahedral algebra
• Super-tetrahedra and super-algebras
• Explicit R-matrices for inhomogeneous 3D chiral Potts models: Integrability and the action formulation for