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The Lax pair for the fermionic Bazhanov-Stroganov \(R\)-operator. (English) Zbl 1476.81103

Summary: We derive the Lax connection of the free fermion model on a lattice starting from the fermionic formulation of Bazhanov-Stroganov’s three-parameter elliptic parametrization for the R-operator. It results in the Yang-Baxter and decorated Yang-Baxter equations of difference type in one of the spectral parameters, which is the most suitable form to obtain any relativistic model of free fermions in the continuous limit.

MSC:

81T35 Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.)
81Q80 Special quantum systems, such as solvable systems
81V74 Fermionic systems in quantum theory
81T27 Continuum limits in quantum field theory
16T25 Yang-Baxter equations
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
81R20 Covariant wave equations in quantum theory, relativistic quantum mechanics
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