Fermionization and Hubbard Models

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.Comment: 24 pages, Latex. Minor typos corrected, one equation adde

Exact integrability of the su(n) Hubbard model

The bosonic su(n) Hubbard model was recently introduced. The model was shown to be integrable in one dimension by exhibiting the infinite set of conserved quantities. I derive the R-matrix and use it to show that the conserved charges commute among themselves. This new matrix is a non-additive solution of the Yang-Baxter equation. Some properties of this matrix are derived.Comment: 6 pages, LaTeX. One reference adde

Multiplicity in Supersymmetric Spin Chains

We discuss a simple procedure for obtaining new integrable spin chains from old by replacing each single state of the original model by some collection of states. This works whenever the Lax matrix of the chain has a certain form. The simplest example is the su(n) XX model. We apply the techniques of the nested algebraic Bethe ansatz to solve such systems, in the bosonic and supersymmetric cases.Comment: 14 pages. v2: Added references and minor corrections; v3: Acknowledgement adde

Integrable open boundary conditions for XXC models

The XXC models are multistate generalizations of the well known spin 1/2 XXZ model. These integrable models share a common underlying su(2) structure. We derive integrable open boundary conditions for the hierarchy of conserved quantities of the XXC models . Due to lack of crossing unitarity of the R-matrix, we develop specific methods to prove integrability. The symmetry of the spectrum is determined.Comment: Latex2e, 10 page

On the integrability of the SU(N) Hubbard model

We exhibit explicitly the intertwiner operator for the monodromy matrices of the recent proposed SU(N) Hubbard model [5]. This produces a new family of non-additive R-matrices and generalizes an earlier result by Shastry [2].Comment: 4 page

Logarithmic Yangians in WZW models

A new action of the Yangians in the WZW models is displayed. Its structure is generic and level independent. This Yangian is the natural extension at the conformal point of the one unravelled in massive theories with current algebras. Expectingly, this new symmetry of WZW models will lead to a deeper understanding of the integrable structure of conformal field theories and their deformations.Comment: 8 pages, TeX, harvmac, 2 .eps figure