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

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

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

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

Non-additive fusion, Hubbard models and non-locality

In the framework of quantum groups and additive R-matrices, the fusion procedure allows to construct higher-dimensional solutions of the Yang-Baxter equation. These solutions lead to integrable one-dimensional spin-chain Hamiltonians. Here fusion is shown to generalize naturally to non-additive R-matrices, which therefore do not have a quantum group symmetry. This method is then applied to the generalized Hubbard models. Although the resulting integrable models are not as simple as the starting ones, the general structure is that of two spin-(s times s') sl(2) models coupled at the free-fermion point. An important issue is the probable lack of regular points which give local Hamiltonians. This problem is related to the existence of second order zeroes in the unitarity equation, and arises for the XX models of higher spins, the building blocks of the Hubbard models. A possible connection between some Lax operators L and R-matrices is noted.Comment: 14 pages, Latex. A remark added in section 2, four typos correcte

On the Solution of Topological Landau-Ginzburg Models with c=3c=3

The solution is given for the $c=3$ topological matter model whose underlying conformal theory has Landau-Ginzburg model W=-\qa (x^4 +y^4)+\af x^2y^2. While consistency conditions are used to solve it, this model is probably at the limit of such techniques. By using the flatness of the metric of the space of coupling constants I rederive the differential equation that relates the parameter \af\ to the flat coordinate $t$. This simpler method is also applied to the $x^3+y^6$-model.Comment: 7p

New Integrable Models from Fusion

Integrable multistate or multiflavor/color models were recently introduced. They are generalizations of models corresponding to the defining representations of the U_q(sl(m)) quantum algebras. Here I show that a similar generalization is possible for all higher dimensional representations. The R-matrices and the Hamiltonians of these models are constructed by fusion. The sl(2) case is treated in some detail and the spin-0 and spin-1 matrices are obtained in explicit forms. This provides in particular a generalization of the Fateev-Zamolodchikov Hamiltonian.Comment: 11 pages, Latex. v2: statement concerning symmetries qualified, 3 minor misprints corrected. J. Phys. A (1999) in pres