38 research outputs found
Twisted Quantum Affine Superalgebra , Invariant R-matrices and a New Integrable Electronic Model
We describe the twisted affine superalgebra and its quantized
version . We investigate the tensor product representation
of the 4-dimensional grade star representation for the fixed point
subsuperalgebra . We work out the tensor product decomposition
explicitly and find the decomposition is not completely reducible. Associated
with this 4-dimensional grade star representation we derive two
invariant R-matrices: one of them corresponds to and the
other to . Using the R-matrix for , we
construct a new invariant strongly correlated electronic model,
which is integrable in one dimension. Interestingly, this model reduces, in the
limit, to the one proposed by Essler et al which has a larger, ,
symmetry.Comment: 17 pages, LaTex fil
Solutions of the Yang-Baxter Equation with Extra Non-Additive Parameters II: }
The type-I quantum superalgebras are known to admit non-trivial one-parameter
families of inequivalent finite dimensional irreps, even for generic . We
apply the recently developed technique to construct new solutions to the
quantum Yang-Baxter equation associated with the one-parameter family of irreps
of , thus obtaining R-matrices which depend not only on a
spectral parameter but in addition on further continuous parameters. These
extra parameters enter the Yang-Baxter equation in a similar way to the
spectral parameter but in a non-additive form.Comment: 10 pages, LaTex file (some errors in the Casimirs corrected
On Type-I Quantum Affine Superalgebras
The type-I simple Lie-superalgebras are and . We study
the quantum deformations of their untwisted affine extensions
and . We identify additional
relations between the simple generators (``extra -Serre relations") which
need to be imposed to properly define \uqgh and . We
present a general technique for deriving the spectral parameter dependent
R-matrices from quantum affine superalgebras. We determine the R-matrices for
the type-I affine superalgebra in various representations,
thereby deriving new solutions of the spectral-dependent Yang-Baxter equation.
In particular, because this algebra possesses one-parameter families of
finite-dimensional irreps, we are able to construct R-matrices depending on two
additional spectral-like parameters, providing generalizations of the
free-fermion model.Comment: 23 page
A New Supersymmetric and Exactly Solvable Model of Correlated Electrons
A new lattice model is presented for correlated electrons on the unrestricted
-dimensional electronic Hilbert space (where
is the lattice length). It is a supersymmetric generalization of the
Hubbard model, but differs from the extended Hubbard model proposed by Essler,
Korepin and Schoutens. The supersymmetry algebra of the new model is
superalgebra . The model contains one symmetry-preserving free real
parameter which is the Hubbard interaction parameter , and has its origin
here in the one-parameter family of inequivalent typical 4-dimensional irreps
of . On a one-dimensional lattice, the model is exactly solvable by
the Bethe ansatz.Comment: 10 pages, LaTex. (final version to appear in Phys.Rev.Lett.
Type-I Quantum Superalgebras, -Supertrace and Two-variable Link Polynomials
A new general eigenvalue formula for the eigenvalues of Casimir invariants,
for the type-I quantum superalgebras, is applied to the construction of link
polynomials associated with {\em any} finite dimensional unitary irrep for
these algebras. This affords a systematic construction of new two-variable link
polynomials asociated with any finite dimensional irrep (with a real highest
weight) for the type-I quantum superalgebras. In particular infinite families
of non-equivalent two-variable link polynomials are determined in fully
explicit form.Comment: the version to be published in J. Math. Phy
Integrable Electron Model with Correlated Hopping and Quantum Supersymmetry
We give the quantum analogue of a recently introduced electron model which
generalizes the Hubbard model with additional correlated hopping terms and
electron pair hopping. The model contains two independent parameters and is
invariant with respect to the quantum superalgebra . It is
integrable in one dimension by means of the quantum inverse scattering method.Comment: 7 pages, AmsTex fil
Exact solutions for a family of spin-boson systems
We obtain the exact solutions for a family of spin-boson systems. This is
achieved through application of the representation theory for polynomial
deformations of the Lie algebra. We demonstrate that the family of
Hamiltonians includes, as special cases, known physical models which are the
two-site Bose-Hubbard model, the Lipkin-Meshkov-Glick model, the molecular
asymmetric rigid rotor, the Tavis-Cummings model, and a two-mode generalisation
of the Tavis-Cummings model.Comment: LaTex 15 pages. To appear in Nonlinearit
Integrable multiparametric quantum spin chains
Using Reshetikhin's construction for multiparametric quantum algebras we
obtain the associated multiparametric quantum spin chains. We show that under
certain restrictions these models can be mapped to quantum spin chains with
twisted boundary conditions. We illustrate how this general formalism applies
to construct multiparametric versions of the supersymmetric t-J and U models.Comment: 17 pages, RevTe