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Journal of the Physical Society of Japan

Yang-Baxter Relations for Spin Models and Fermion Models

Eugenio Olmedilla, Miki Wadati, Yasuhiro Akutsu

Published Jul 15, 1987• 88 citations
Publisher

Abstract

A systematic method to derive the Yang-Baxter relations for the fermion models which are equivalent to the solvable spin models is presented. The method is applied to prove the Yang-Baxter relation and the commutability of the transfer matrices for the one-dimensional Hubbard model.
DOI
10.1143/jpsj.56.2298

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The 1D Hubbard model is shown to be an exactly integrable system. A "covering" model of 2D statistical mechanics which I proposed recently was shown to provide a one-parameter family of transfer matrices, commuting with the Hamiltonian of the Hubbard model. I show in this work that any two transfer matrices of a family commute mutually. At the root of the commutation relation is the ubiquitous Yang-Baxter factorization condition. The form of the RRR operator is displayed explicitly.
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