Generalization of the U_q(gl(N)) algebra and staggered models

We develop a technique of construction of integrable models with a Z_2 grading of both the auxiliary (chain) and quantum (time) spaces. These models have a staggered disposition of the anisotropy parameter. The corresponding Yang-Baxter Equations are written down and their solution for the gl(N) case are found. We analyze in details the N=2 case and find the corresponding quantum group behind this solution. It can be regarded as quantum U_{q,B}(gl(2)) group with a matrix deformation parameter qB with (qB)^2=q^2. The symmetry behind these models can also be interpreted as the tensor product of the (-1)-Weyl algebra by an extension of U_q(gl(N)) with a Cartan generator related to deformation parameter -1.Comment: 12 pages ; Latex2

Lattice electrons in constant magnetic field: Bethe like ansatz

We use the functional representation of Heisenberg-Weyl group and obtain equation for the spectrum of the model, which is more complicated than Bethes ones, but can be written explicitly through theta functions.Comment: 8 pages, LATE

Crossover from weak localization to Shubnikov-de Haas oscillations in a high mobility 2D electron gas

We study the magnetoresistance, \delta\rho_{xx}(B)/\rho_0, of a high-mobility 2D electron gas in the domain of magnetic fields, B, intermediate between the weak localization and the Shubnikov-de Haas oscillations, where \delta\rho_{xx}(B)/\rho_0 is governed by the interaction effects. Assuming short-range impurity scattering, we demonstrate that in the {\em second order} in the interaction parameter, $\lambda$, a {\em linear} B-dependence, \delta\rho_{xx}(B)/\rho_0\sim \lambda^2\omega_c/E_F with {\em temperature-independent} slope emerges in this domain of B (here \omega_c and E_F are the cyclotron frequency and the Fermi energy, respectively). Unlike previous mechanisms, the linear magnetoresistance is {\em unrelated} to the electron executing the full Larmour circle, but rather originates from the impurity scattering via the B-dependence of the {\em phase} of the impurity-induced Friedel oscillations.Comment: 4+ pages, 3 figure

Bethe Ansatz and Thermodynamic Limit of Affine Quantum Group Invariant Extensions of the t-J Model

We have constructed a one dimensional exactly solvable model, which is based on the t-J model of strongly correlated electrons, but which has additional quantum group symmetry, ensuring the degeneration of states. We use Bethe Ansatz technique to investigate this model. The thermodynamic limit of the model is considered and equations for different density functions written down. These equations demonstrate that the additional colour degrees of freedom of the model behave as in a gauge theory, namely an arbitrary distribution of colour indices over particles leave invariant the energy of the ground state and the excitations. The $S$-matrix of the model is shown to be the product of the ordinary $t-J$ model $S$-matrix and the unity matrix in the colour space.Comment: Latex, 17 page