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

Integrability and exact solution for coupled BCS systems associated with the su(4)su(4) Lie algebra

We introduce an integrable model for two coupled BCS systems through a solution of the Yang-Baxter equation associated with the Lie algebra $su(4)$. By employing the algebraic Bethe ansatz, we determine the exact solution for the energy spectrum. An asymptotic analysis is conducted to determine the leading terms in the ground state energy, the gap and some one point correlation functions at zero temperature.Comment: 15 page

Algebraic Bethe ansatz for the one-dimensional Hubbard model with open boundaries

The one-dimensional Hubbard model with open boundary conditions is exactly solved by means of algebraic Bethe ansatz. The eigenvalue of the transfer matrix, the energy spectrum as well as the Bethe ansatz equations are obtained.Comment: Only LaTex file; no figur

Generalised Perk--Schultz models: solutions of the Yang-Baxter equation associated with quantised orthosymplectic superalgebras

The Perk--Schultz model may be expressed in terms of the solution of the Yang--Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra $U_q[sl(m|n)]$, with a multiparametric co-product action as given by Reshetikhin. Here we present analogous explicit expressions for solutions of the Yang-Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras $U_q[osp(m|n)]$. In this manner we obtain generalisations of the Perk--Schultz model.Comment: 10 pages, 2 figure

Integrability of a t-J model with impurities

A t-J model for correlated electrons with impurities is proposed. The impurities are introduced in such a way that integrability of the model in one dimension is not violated. The algebraic Bethe ansatz solution of the model is also given and it is shown that the Bethe states are highest weight states with respect to the supersymmetry algebra gl(2/1)Comment: 14 page

Exactly solvable models and ultracold Fermi gases

Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe Ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirm that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.Comment: based on an invited talk at Statphys24, Cairns (Australia) 2010. 16 pages, 6 figure

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

The Phase Diagram and Spectrum of Gauge-Fixed Abelian Lattice Gauge Theory

We consider a lattice discretization of a covariantly gauge-fixed abelian gauge theory. The gauge fixing is part of the action defining the theory, and we study the phase diagram in detail. As there is no BRST symmetry on the lattice, counterterms are needed, and we construct those explicitly. We show that the proper adjustment of these counterterms drives the theory to a new type of phase transition, at which we recover a continuum theory of (free) photons. We present both numerical and (one-loop) perturbative results, and show that they are in good agreement near this phase transition. Since perturbation theory plays an important role, it is important to choose a discretization of the gauge-fixing action such that lattice perturbation theory is valid. Indeed, we find numerical evidence that lattice actions not satisfying this requirement do not lead to the desired continuum limit. While we do not consider fermions here, we argue that our results, in combination with previous work, provide very strong evidence that this new phase transition can be used to define abelian lattice chiral gauge theories.Comment: 42 pages, 30 figure