Simplified tetrahedron equations: Fermionic realization
J. Ambjorn, Sh.Khachatryan, A.Sedrakyan
TL;DR
This paper introduces a simplified version of the three-dimensional Zamolodchikov tetrahedron equations, providing a family of free fermionic solutions that maintain transfer matrix commutativity with spectral parameters.
Contribution
It presents a novel simplified form of the tetrahedron equations along with explicit free fermionic solutions, advancing understanding of three-dimensional integrable models.
Findings
Provided a family of free fermionic solutions to the simplified tetrahedron equations.
Ensured the commutativity of transfer matrices with different spectral parameters.
Extended the framework of integrable models to a simplified three-dimensional setting.
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.
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