Fermionization and Hubbard Models

TL;DR

This paper presents a universal fermionization transformation for one-dimensional spin chains, enabling new insights into symmetries, integrability, and the fermionic form of Hubbard and higher-spin models.

Contribution

Introduces a general fermionization method for 1D spin chains, applicable to integrable and non-integrable models, and derives multispecies Hubbard models in fermionic form.

Findings

Fermionization of XXC spin-chains and analysis of their symmetries.

Fermionic realizations of Lie algebras and superalgebras as model symmetries.

First fermionic form of multispecies Hubbard models.

Abstract

We introduce a transformation which allows the fermionization of operators of any one-dimensional spin-chain. This fermionization procedure is independent of any eventual integrable structure and is compatible with it. We illustrate this method on various integrable and non-integrable chains, and deduce some general results. In particular, we fermionize XXC spin-chains and study their symmetries. Fermionic realizations of certain Lie algebras and superalgebras appear naturally as symmetries of some models. We also fermionize recently obtained Hubbard models, and obtain for the first time multispecies analogues of the Hubbard model, in their fermionic form. We comment on the conflict between symmetry enhancement and integrability of these models. Finally, the fermionic versions of the non integrable spin-1 and spin-3/2 Heisenberg chains are obtained.