On the fermionization of the XYZ spin Heisenberg chain (algebra).

Abstract

We present a generalization of the Yang-Baxter relation (relations (9), our first point) applicable to a onedimensional asymmetric chain (XYZ) with creation and annihilation operators for fermions, instead of the usual relation with spins. The role of a sign associated to the modulus k of the Jacobi elliptic functions is crucial. We obtain a special property relating the products of local transition matrices with fermion operators and the terms of the Hamiltonian (equations in (22), our second point). With these two ground stages we prove the existence of a set of commuting quantities, among them our proposed Hamiltonian of an asymmetric fermión chain.