Solution of a two-leg spin ladder system

A model for a spin-1/2 ladder system with two legs is introduced. It is demonstrated that this model is solvable via the Bethe ansatz method for arbitrary values of the rung coupling J. This is achieved by a suitable mapping from the Hubbard model with appropriate twisted boundary conditions. We determine that a phase transition between gapped and gapless spin excitations occurs at the critical value J(c) = 1/2 of the rung coupling.

Level-one highest weight representation of U-q[sl((N)over-cap vertical bar 1)] and Bosonization of the multicomponent Super t-J model

We study the level-one irreducible highest weight representations of the quantum affine superalgebra U-q[sl((N) over cap\1)], and calculate their characters and supercharacters. We obtain bosonized q-vertex operators acting on the irreducible U-q[sl((N) over cap\1)] modules and derive the exchange relations satisfied by the vertex operators. We give the bosonization of the multicomponent super t-J model by using the bosonized vertex operators. (C) 2000 American Institute of Physics. [S0022- 2488(00)00508-9].

Integrable Kondo impurities in one-dimensional extended Hubbard models

Three kinds of integrable Kondo problems in one-dimensional extended Hubbard models are studied by means of the boundary graded quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras acting in a (2s alpha + 1)-dimensional impurity Hilbert space. Furthermore, these models are solved using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

Quantum spin ladder systems associated with su(2 vertical bar 2)

Two integrable quantum spin ladder systems will be introduced associated with the fundamental su(2 \2) solution of the Yang-Baxter equation. The first model is a generalized quantum Ising system with Ising rung interactions. In the second model the addition of extra interactions allows us to impose Heisenberg rung interactions without violating integrability. The existence of a Bethe ansatz solution for both models allows us to investigate the elementary excitations for antiferromagnetic rung couplings. We find that the first model does not show a gap whilst in the second case there is a gap for all positive values of the rung coupling.

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 U-q(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.

Integrable Kondo impurity in one-dimensional q-deformed t-J models

Integrable Kondo impurities in two cases of one-dimensional q-deformed t-J models are studied by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, these models are solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.

Integrability and exact solution of an electronic model with long range interactions

We present an electronic model with long range interactions. Through the quantum inverse scattering method, integrability of the model is established using a one-parameter family of typical irreducible representations of gl(211). The eigenvalues of the conserved operators are derived in terms of the Bethe ansatz, from which the energy eigenvalues of the Hamiltonian are obtained.

Signature of mott-insulator transition with ultracold fermions in a one-dimensional optical lattice

Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultracold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.

Integrable extended hubbard models with boundary Kondo impurities

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

Exact solution for the Bariev model with boundary fields

The Bariev model with open boundary conditions is introduced and analysed in detail in the framework of the Quantum Inverse Scattering Method. Two classes of independent boundary reflecting K-matrices leading to four different types of boundary fields are obtained by solving the reflection equations. The models are exactly solved by means of the algebraic nested Bethe ansatz method and the four sets or Bethe ansatz equations as well as their corresponding energy expressions are derived. (C) 2001 Elsevier Science B.V. All rights reserved.

A new integrable model of strongly correlated electrons with Hubbard-like interaction

A new completely integrable model of strongly correlated electrons is proposed which describes two competitive interactions: one is the correlated one-particle hopping, the other is the Hubbard-like interaction. The integrability follows from the fact that the Hamiltonian is derivable from a one-parameter family of commuting transfer matrices. The Bethe ansatz equations are derived by algebraic Bethe ansatz method.

Integrable anisotropic spin-ladder model

We present an integrable spin-ladder model, which possesses a free parameter besides the rung coupling J. Wang's system based on the SU(4) symmetry can be obtained as a special case. The model is exactly solvable by means of the Bethe ansatz method. We determine the dependence on the anisotropy parameter of the phase transition between gapped and gapless spin excitations and present the phase diagram. Finally, we show that the model is a special case of a more general Hamiltonian with three free parameters.

Izergin-Korepin model with a boundary

The Izergin-Korepin model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the twisted quantum affine algebra U-q[((2))(2)]. We give the bosonization of the vacuum state with zero particle content. Excitation states are given by the action of the vertex operators on the vacuum state. We derive the boundary S-matrix. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy. (C) 2001 Elsevier Science B.V. All rights reserved.

Integrable open boundary conditions for the Bariev model of three coupled X Y spin chains

The integrable open-boundary conditions for the Bariev model of three coupled one-dimensional XY spin chains are studied in the framework of the boundary quantum inverse scattering method. Three kinds of diagonal boundary K-matrices leading to nine classes of possible choices of boundary fields are found and the corresponding integrable boundary terms are presented explicitly. The boundary Hamiltonian is solved by using the coordinate Bethe ansatz technique and the Bethe ansatz equations are derived. (C) 2001 Elsevier Science B.V. All rights reserved.