Twisted Quantum Affine Superalgebra Uq[sl(2∣2)(2)]U_q[sl(2|2)^{(2)}], Uq[osp(2∣2)]U_q[osp(2|2)] Invariant R-matrices and a New Integrable Electronic Model

We describe the twisted affine superalgebra $sl(2|2)^{(2)}$ and its quantized version $U_q[sl(2|2)^{(2)}]$. We investigate the tensor product representation of the 4-dimensional grade star representation for the fixed point subsuperalgebra $U_q[osp(2|2)]$. 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 $U_q[osp(2|2)]$ invariant R-matrices: one of them corresponds to $U_q[sl(2|2)^{(2)}]$ and the other to $U_q[osp(2|2)^{(1)}]$. Using the R-matrix for $U_q[sl(2|2)^{(2)}]$, we construct a new $U_q[osp(2|2)]$ invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly, this model reduces, in the $q=1$ limit, to the one proposed by Essler et al which has a larger, $sl(2|2)$, symmetry.Comment: 17 pages, LaTex fil

Solutions of the Yang-Baxter Equation with Extra Non-Additive Parameters II: Uq(gl(m∣n))U_q(gl(m|n))}

The type-I quantum superalgebras are known to admit non-trivial one-parameter families of inequivalent finite dimensional irreps, even for generic $q$. 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 $U_q(gl(m|n))$, 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

A New Supersymmetric and Exactly Solvable Model of Correlated Electrons

A new lattice model is presented for correlated electrons on the unrestricted $4^L$-dimensional electronic Hilbert space $\otimes_{n=1}^L{\bf C}^4$ (where $L$ 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 $gl(2|1)$. The model contains one symmetry-preserving free real parameter which is the Hubbard interaction parameter $U$, and has its origin here in the one-parameter family of inequivalent typical 4-dimensional irreps of $gl(2|1)$. 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.

On Type-I Quantum Affine Superalgebras

The type-I simple Lie-superalgebras are $sl(m|n)$ and $osp(2|2n)$. We study the quantum deformations of their untwisted affine extensions $U_q(sl(m|n)^{(1)})$ and $U_q(osp(2|2n)^{(1)})$. We identify additional relations between the simple generators (``extra $q$-Serre relations") which need to be imposed to properly define \uqgh and $U_q(osp(2|2n)^{(1)})$. 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 $U_q(sl(m|n)^{(1)})$ 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

Type-I Quantum Superalgebras, qq-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 $U_q(gl(2|1))$. 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 $su(2)$ 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