Fermionization and Hubbard Models

Details Fermionization and Hubbard Models Fermionization and Hubbard Models

1998-06-17

arxiv.org/abs/cond-mat/9806208v2

Nucl.Phys. B535 (1998) 681-708

Physics

Condensed Matter

24 pages, Latex. Minor typos corrected, one equation added

Scientific paper

10.1016/S0550-3213(98)00650-6

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.

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