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R. Z. Bariev

Publications and source records attributed to R. Z. Bariev.

16 recordsLinked to original sources
arXiv2000

Exact Solution of Asymmetric Diffusion With N Classes of Particles of Arbitrary Size and Hierarchical Order

The exact solution of the asymmetric exclusion problem with N distinct classes of particles (c = 1,2,...,N), with hierarchical order is presented. In this model the particles (size 1) are located at lattice points, and diffuse with equal asymmetric rates, but particles in a class c do not distinguish those in the classes c' >c from holes (empty sites). We generalize and solve exactly this model by considering the molecules in each distinct class c =1,2,...,N with sizes s_c (s_c = 0,1,2,...), in units of lattice spacing. The solution is derived by a Bethe ansatz of nested type.

cond-mat.stat-mech↗
arXiv2000

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

The exact solution of the asymmetric exclusion problem with particles of first and second class is presented. In this model the particles (size 1) of both classes are attached on lattice points and diffuse with equal asymmetric rates, but particles in the first class do not distinguish those in the second class from the holes (empty sites). We generalize and solve exactly this model by considering molecules in the first and second class with sizes $s_1$ and $s_2$ ($s_1,s_2 = 0,1,2,...$), in units of lattice spacing, respectively. The solution is derived by a Bethe ansatz of nested type. We give in this paper a pedagogical and simple presentation of the Bethe ansatz solution of the problem which can easily be followed by a non specialized audience in exactly integrable models.

cond-mat.stat-mech↗
arXiv1999

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 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.

cond-mat.stat-mech↗
arXiv1999

New 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.

cond-mat.stat-mech↗
arXiv1999

Exact Solution of the Asymmetric Exclusion Model with Particles of Arbitrary Size

A generalization of the simple exclusion asymmetric model is introduced. In this model an arbitrary mixture of molecules with distinct sizes $s = 0,1,2,...$, in units of lattice space, diffuses asymmetrically on the lattice. A related surface growth model is also presented. Variations of the distribution of molecules's sizes may change the excluded volume almost continuously. We solve the model exactly through the Bethe ansatz and the dynamical critical exponent $z$ is calculated from the finite-size corrections of the mass gap of the related quantum chain. Our results show that for an arbitrary distribution of molecules the dynamical critical behavior is on the Kardar-Parizi-Zhang (KPZ) universality.

cond-mat.stat-mech↗
arXiv1999

An Exactly Solvable Constrained XXZ Chain

A new family of exactly solvable models is introduced. These models are generalizations of the XXZ chain where the distance among spins up ($σ^z$-basis) cannot be smaller or equal to t (t=0,1,2,...). The case t=0 recovers the standard XXZ chain. The coordinate Bethe ansatz is applied and the phase diagram is calculated. Exploring the finite-size consequences of conformal invariance the critical exponents are evaluated exactly at the critical regions of the phase diagram

cond-mat.stat-mech↗
arXiv1999

New integrable version of the degenerate supersymmetric t-J model

A new integrable version of the degenerate supersymmetric t-J model is proposed. In this formulation instead of restricting 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 anzatz.

cond-mat.stat-mech↗
arXiv1999

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.

cond-mat.stat-mech↗
arXiv1997

New Integrable Generalization of the One-Dimensional t-J Model

A new generalization of the t-J model with a nearest-neigbour hopping is formulated and solved exactly by the Bethe-ansatz method in the thermodymanic limit. The model describes the dymanics of fermions with different spins and with isotropic and anisotropic interactions.

cond-mat.stat-mech↗
arXiv1997

Phase Diagram and Superconducting Properties of an Exactly Solvable Model with Correlated Hopping

The model of strongly correlated electrons with the correlated hopping term and an additional interaction between holes $V$ is solved exactly in one dimension at a special point where the number of hole pairs is conserved. As a function of the interaction $V$ the phase diagram has a rich structure. There exist gapless phases with dominating density-density correlations (metallic) or pair-pair correlations (superconducting) as well insulating and phase-separated phases. The stiffness constant of the conductivity, the effective transport mass, and the compressibility are also exactly calculated in several regions of the phase diagram.

cond-mat.stat-mech↗
arXiv1997

Exact Solution of the Biquadratic Spin-1 t-J Model in One Dimension

A new generalization of the t-J model with a nearest-neigbor hopping is formulated and solved exactly by the Bethe-ansatz method. The model describes the dynamics of spin-S fermions with isotropic or anisotropic interactions. In the case S=1 the magnetic interaction is biquadratic in the spin operators. In contrast to the SU(N) generalization of the t-J model, studied previously in the literature, the present model possesses beyond a massless excitation also a massive one. The physical properties indicate the existence of Cooper-type pairs with finite binding energy.

cond-mat.stat-mech↗
arXiv1995

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.

cond-mat↗
arXiv1994

Critical exponents of a multicomponent anisotropic t-J model in one dimension

A recently presented anisotropic generalization of the multicomponent supersymmetric $t-J$ model in one dimension is investigated. This model of fermions with general spin-$S$ is solved by Bethe ansatz for the ground state and the low-lying excitations. Due to the anisotropy of the interaction the model possesses $2S$ massive modes and one single gapless excitation. The physical properties indicate the existence of Cooper-type multiplets of $2S+1$ fermions with finite binding energy. The critical behaviour is described by a $c=1$ conformal field theory with continuously varying exponents depending on the particle density. There are two distinct regimes of the phase diagram with dominating density-density and multiplet-multiplet correlations, respectively. The effective mass of the charge carriers is calculated. In comparison to the limit of isotropic interactions the mass is strongly enhanced in general.

cond-mat↗
arXiv1994

Exact solution of a one-dimensional fermion model with interchain tunneling

A fermion model consisting of two chains with interchain tunneling is formulated and solved exactly by the Bethe ansatz method. The interchain tunneling leads to Cooper pair like bound states and a threshold energy is required to overcome the binding energy. The correlation functions manifest superconducting properties.

cond-mat↗
arXiv1993

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 groundstate 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.

cond-mat↗