R. Z. Bariev

A NEW INTEGRABLE TWO-PARAMETER MODEL OF STRONGLY CORRELATED ELECTRONS IN ONE DIMENSION

A new one-dimensional fermion model depending on two independent interaction parameters is formulated and solved exactly by the Bethe-ansatz method. The Hamiltonian of the model contains the Hubbard interaction and correlated hopping as well as pair hopping terms. The density-density and pair correlations are calculated which manifest superconducting properties in certain regimes of the phase diagram.

Interpolation between Hubbard and supersymmetric t-J models: two-parameter integrable models of correlated electrons

Two new one-dimensional fermionic models depending on two independent parameters are formulated and solved exactly by the Bethe ansatz method. These models connect continuously the integrable Hubbard and supersymmetric t-J models.

Exact solution of asymmetric diffusion with second-class particles of arbitrary size

The exact solution of the asymmetric exclusion problem with first- and scond-class particles is presented. In this model the particles (size 1) of both classes are located at lattice points, and diffuse with equal asymmetric rates, but particles in the first class do not distinguish those in the second class from holes (empty sites). We generalize and solve exactly this model by considering molecules in the first and second class with sizes s1 and s2 (s1, s2 = 0, 1, 2, ...), in units of lattice spacing, respectively. The solution is derived by a Bethe ansatz of nested type. We give a simple pedagogical presentation of the Bethe ansatz solution of the problem which can easily be followed by a reader not specialized in exactly integrable models.

Excitation spectrum and critical exponents of a one-dimensional integrable model of fermions with correlated hopping

We investigate the excitation spectrum of a model of N colour fermions with correlated hopping which can be solved by a nested Bethe ansatz. The gapless excitations of particle-hole type are calculated as well as the spin-wave like excitations which have a gap. Using general predictions of conformal field theory the long distance behaviour of some ground state correlation functions are derived from a finite-size analysis of the gapless excitations. From the algebraic decay we show that for increasing particle density the correlation of so-called N-multiplets of particles dominates over the density-density correlation. This indicates the presence of bound complexes of these N-multiplets. This picture is also supported by the calculation of the effective mass of charge carriers.

New exact integrable spin-1 quantum chains

New exactly integrable quantum spin-1 chains are derived. These new quantum Hamiltonians, like the XXZ chain, have a free parameter (anisotropy) and commute with the z-component of the total magnetization. The eigenvalues and eigenvectors are obtained directly by imposing a generalized coordinate Bethe ansatz. The derived Bethe ansatz equations have an unusual form and the associated R-matrix, has a dependence with the spectral parameter that is not of difference form, like the Hubbard quantum chain.

INTEGRABLE MODELS OF STRONGLY CORRELATED PARTICLES WITH CORRELATED HOPPING

The exact solution is obtained for the eigenvalues and eigenvectors for two models of strongly correlated particles with single-particle correlated and uncorrelated pair hoppings. The asymptotic behavior of correlation functions are analysed in different regions, where the models exhibit different physical behavior.

Two-dimensional Ising model and local nonuniversality of critical exponents

We obtain the local magnetization of a planar Ising model with defects of different types. It is shown that near the critical point the local magnetization has a nonuniversal behavior that manifests itself in the fact that its critical exponent is a continuous function of the microscopic parameters of the system.

Exact solution of a vertex model with unlimited number of states per bond

The exact solution is obtained for the eigenvalues and eigenvectors of the row-to-row transfer matrix of a two-dimensional vertex model with unlimited number of states per bond. This model is a classical counterpart of a quantum spin chain with an unlimited value of spin. This quantum chain is studied using general predictions of conformal field theory. The long-distance behaviour of some ground-state correlation functions is derived from a finite-size analysis of the gapless excitations.

New integrable version of the degenerate supersymmetric t-J model

Abstract A new integrable version of the degenerate supersymmetric t-J model is proposed. In this formulation, instead of restricting the single occupancy of electrons at each lattice site we may have up to two electrons at each site. As a requirement of exact integrability the hopping interaction turns out to be correlated with the density of electrons in the neighboring sites. The exact solution of the model is obtained through the coordinate Bethe ansatz.

Integrable model of interacting XX and Fateev-Zamolodchikov chains

We consider the exact solution of a model of correlated particles, which is presented as a system of interacting XX and Fateev-Zamolodchikov chains. This model can also be considered as a generalization of the multiband anisotropic t-J model in the case where we restrict the site occupations to at most two electrons. The exact solution is obtained for the eigenvalues and eigenvectors using the Bethe ansatz method.