508 research outputs found
Twisting invariance of link polynomials derived from ribbon quasi-Hopf algebras
The construction of link polynomials associated with finite dimensional
representations of ribbon quasi-Hopf algebras is discussed in terms of the
formulation of an appropriate Markov trace. We then show that this Markov trace
is invariant under twisting of the quasi-Hopf structure, which in turn implies
twisting invariance of the associated link polynomials.Comment: 18 pages, LaTeX, no figure
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.
Bethe ansatz solution of the anisotropic correlated electron model associated with the Temperley-Lieb algebra
A recently proposed strongly correlated electron system associated with the
Temperley-Lieb algebra is solved by means of the coordinate Bethe ansatz for
periodic and closed boundary conditions.Comment: 21 page
Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(2|n)]
Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so
contains a \textit{universal -matrix} in the tensor product algebra which
satisfies the Yang-Baxter equation. Applying the vector representation ,
which acts on the vector module , to one side of a universal -matrix
gives a Lax operator. In this paper a Lax operator is constructed for the
-type quantum superalgebras . This can in turn be used to
find a solution to the Yang-Baxter equation acting on
where is an arbitrary module. The case is included
here as an example.Comment: 15 page
Eigenvalus of Casimir Invariants for Type-I Quantum Superalgebras
We present the eigenvalues of the Casimir invariants for the type I quantum
superalgebras on any irreducible highest weight module.Comment: 13 pages, AmsTex file; to appear in Lett. Math. Phy
A variational approach for the Quantum Inverse Scattering Method
We introduce a variational approach for the Quantum Inverse Scattering Method
to exactly solve a class of Hamiltonians via Bethe ansatz methods. We undertake
this in a manner which does not rely on any prior knowledge of integrability
through the existence of a set of conserved operators. The procedure is
conducted in the framework of Hamiltonians describing the crossover between the
low-temperature phenomena of superconductivity, in the
Bardeen-Cooper-Schrieffer (BCS) theory, and Bose-Einstein condensation (BEC).
The Hamiltonians considered describe systems with interacting Cooper pairs and
a bosonic degree of freedom. We obtain general exact solvability requirements
which include seven subcases which have previously appeared in the literature.Comment: 18 pages, no eps figure
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
Transfer matrix eigenvalues of the anisotropic multiparametric U model
A multiparametric extension of the anisotropic U model is discussed which
maintains integrability. The R-matrix solving the Yang-Baxter equation is
obtained through a twisting construction applied to the underlying Uq(sl(2|1))
superalgebraic structure which introduces the additional free parameters that
arise in the model. Three forms of Bethe ansatz solution for the transfer
matrix eigenvalues are given which we show to be equivalent.Comment: 26 pages, no figures, LaTe
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