85 research outputs found

### 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 $c=3$

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

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