Deformed Hubbard operator, bosonization, and phase diagram of the one-dimensional t-J model

Journal ArticleWe present an analytic study of the phase diagram of the one-dimensional t-J model and a couple of its cousins. To deal with the interactions induced by the no double occupancy constraints, we introduce a deformation of the Hubbard operators. When the deformation parameter ∆ is small, the induced interactions are softened, accessible by perturbation theory.We combine bosonization with renormalization group techniques to map out the phase diagram of the system. We argue that when ∆ →1, there is no essential change in the phase diagram. A comparison with the existing results in the literature obtained by other methods justifies our deformation approach

Quantum phase transition in a multicomponent Bose-Einstein condensate in optical lattices

Journal ArticleWe present a general lattice model for a multicomponent atomic Bose-Einstein system in an optical lattice. Using the model, we analytically study the quantum phase transition between the Mott insulator and a superfluid. A mean-field theory is developed from the Mott-insulator ground state. When the interspecies interactions are strong enough, the Mott insulator demonstrates the phase separation behavior. For weak interspecies interactions, the multispecies system is miscible. Finally, the phase diagram is discussed with emphasis on the role of interspecies interactions. The tip and the shape of the Mott insulator lobes do not depend on the interspecies interactions, but the latter indeed modify the position of the phase boundaries

On gauge invariance of noncommutative Chern-Simons theories

ManuscriptMotivated by possible applications to condensed matter systems, in this paper we construct U(N) noncommutative Chern-Simons (NCCS) action for a disc and for a double-layer geometry, respectively. In both cases, gauge invariance severely constrains the form of the NCCS action. In the first case, it is necessary to introduce a group-valued boson field with a non-local chiral boundary action, whose gauge variation cancels that of the bulk action. In the second case, the coefficient matrix K in the double U(N) NCCS action is restricted to be of the form K = k (1 1) ( 1 1) with integer k. We suggest that this double NCCS theory with U(1) gauge group describes the so-called Halperin (kkk) state in a double-layer quantum Hall system. Possible physical consequences are addressed

Role of spin-orbit coupling in the metal-insulator transition in two-dimensional systems

Journal ArticleWe propose an experiment, which would allow us to pinpoint the role of spin-orbit coupling in the metal-nonmetal transition observed in a number of two-dimensional systems at low densities. Namely, we demonstrate that in a parallel magnetic field the interplay between the spin-orbit coupling and the Zeeman splitting leads to a characteristic anisotropy of resistivity with respect to the direction of the in-plane magnetic field. Though our analytic calculation is done in the deeply insulating regime, the anisotropy is expected to persist far beyond that regime