Bariev Model Research Articles

Edge singularities in the one-dimensional Bariev model

Bariev's model for correlated hopping in one dimension is integrable and soluble within the framework of two nested Bethe Ansätze. For repulsive interaction and finite magnetization the low energy excitation spectrum is a two-component Luttinger liquid with conformal charges c=1. In zero magnetic field the spectrum of spin excitations is gapped. For higher energy excitations the single-hole (single-particle) spectral functions display edge singularities that deviate from those expected from a Luttinger liquid. The system can be described as a mobile impurity coupled to the Luttinger liquid yielding an effective x-ray edge type model. Using the Bethe Ansatz solution for repulsive interaction we obtain expressions for the critical exponents for the single-particle and single-hole Green's functions in zero magnetic field.

The Effect of a Long-Range Correlated-Hopping Interaction on Bariev Spin Chains

We introduce a long-range particle and spin interaction into the standard Bariev model and show that this interaction is equivalent to a phase shift in the kinetic term of the Hamiltonian. When the particles circle around the chain and across the boundary, the accumulated phase shift acts as a twist boundary condition with respect to the normal periodic boundary condition. This boundary phase term depends on the total number of particles in the system and also the number of particles in different spin states, which relates to the spin fluctuations in the system. The model is solved exactly via a unitary transformation by the coordinate Bethe ansatz. We calculate the Bethe equations and work out the energy spectrum with varying number of particles and spins.

Critical behavior of the spin correlation function in the Ashkin-Teller and Baxter models with a line defect

We consider the critical spin-spin correlation function of the Ashkin-Teller and Baxter models. By using path-integral techniques in the continuum description of these models in terms of fermion fields, we show that the correlation decays with distance with the same critical exponent as the Ising model. The procedure is straightforwardly extended to take into account the presence of a line defect. Thus we find that in these altered models the critical index of the magnetic correlation on the defect coincides with the one of the defective two-dimensional Ising or Bariev model.

General Solutions of Reflection Equations for Bariev Model

The integrable general open-boundary conditions for the one-dimensional Bariev chain are considered. All kinds of solutions to the reflection equation (RE) and its dual are obtained.

Exact Solutions of One-Dimensional N-ComponentBariev Model with General Boundary Conditions

The N-component Bariev model for correlated hopping with openboundary conditions in one dimension is studied in the frameworkof coordinate Bethe ansatz method. The energy spectrum, integrableboundary conditions and the corresponding Bethe ansatz equations are derived.

Thermodynamics of 1D N-Component Bariev ModelUnder Open Boundary Conditions

The thermodynamic Bethe ansatz equations and free energy for 1DN-component Bariev model under open boundary conditions arederived based on the string hypothesis for both, a repulsiveand an attractive interaction. These equations are discussedin some limiting cases, such as the ground state, weak and strong couplings.

Exact Solution of the One-Dimensional N-Component BarievModel with a Hard-Core Repulsion under Open Boundary Conditions

We analyse the integrable boundary conditions for the one-dimensionalN-component generalized Bariev model with a hard-core repulsion. TheBethe ansatz equations and the energy spectrum are obtained in theframework of the nested Bethe ansatz method.

Integrability of N-Component Bariev Model UnderOpen Boundary Conditions

N-component Bariev model for correlated hopping under openboundary conditions in one dimension is studied in the framework ofBethe ansatz method. The energy spectrum and the related Betheansatz equations are obtained.

Boundary Effects for One-Dimensional Bariev Model with Hard-Core Repulsion**The project supported by National Natural Science Foundation of China under Grant No. 90103001

For the Bariev model for correlated hopping in one dimension under open boundary conditions, the Bethe ansatz equations are analyzed for both a repulsive and an attractive interaction in several limiting cases, i.e., the ground state, the weak and strong coupling limits. The contributions of the boundary fields to both the magnetic susceptibility and the specific heat are obtained.

Integrability of the Bariev Model with a Hard Core under OpenBoundary Conditions

For the Bariev model with single electron hopping, pair hopping andhard core potential, we prove the integrability of this model under openboundary conditions and obtained the Bethe ansatz equations by usingthe reflection equations of the open-boundary XXZ model.

Bariev model for correlated hopping with crystalline field splitting

The Bethe Ansatz solution of the one-dimensional Bariev model for correlated hopping for two orbital and two spin degrees of freedom per site is used to study the evolution of the electron bands as a function of crystalline field splitting $\ensuremath{\Delta}.$ The formation of charge bound states (nonlocal Cooper pairs) leads to a charge sector with Fermi surface, while all other excitations are gapped in the absence of fields. The gap for the interband transitions is gradually closed with increasing $\ensuremath{\Delta}.$ Two critical fields ${\ensuremath{\Delta}}_{1}$ and ${\ensuremath{\Delta}}_{2}$ $({\ensuremath{\Delta}}_{1}<{\ensuremath{\Delta}}_{2})$ have to be distinguished. For two electrons per site the system is a one-component Luttinger liquid if $\ensuremath{\Delta}<{\ensuremath{\Delta}}_{1},$ a two-component Luttinger liquid for ${\ensuremath{\Delta}}_{1}<\ensuremath{\Delta}<{\ensuremath{\Delta}}_{2},$ and an insulator for $\ensuremath{\Delta}>{\ensuremath{\Delta}}_{2}.$ The critical behavior of superconducting fluctuations is also discussed.

Integrable one-dimensional N-component fermion model with correlated hopping and hard-core repulsion

The N-component Bariev model for correlated hopping and a hard-core repulsion is shown to be integrable in one dimension. The solution of the model is obtained within the framework of nested Bethe ansatze. The ground state integral equations for the densities of the rapidities are derived for repulsive and attractive correlations. In zero-field and for a repulsive interaction the spin excitations are gapped and only the charge sector has a Fermi surface. The properties are then those of a one-component Luttinger liquid. The spin-gaps are gradually closed with increasing magnetic field. For an attractive interaction potential charge bound states (generalized non-local Cooper pairs) are formed and the spin excitations are gapped in zero magnetic field. The ground state properties and the critical exponents of correlation functions are discussed for both, repulsive and attractive, potentials. The string hypothesis is invoked to derive the thermodynamic Bethe ansatz equations. Some special limits of the thermodynamic equations are analyzed, e.g., the weak and strong interaction cases, and the low and high temperature limits.

Exact solution of the Bariev model for correlated hopping with hard-core repulsion

We present the exact solution of a generalized Bariev model for correlated hopping with a finite-range hard-core repulsion in one dimension. The Bethe ansatz equations and the thermodynamics are derived and analyzed for repulsive and attractive potential. The ground state, the low-energy excitations, the high-temperature limit, and the weak- and strong-coupling limits are discussed as functions of the range of the hard-core exclusion and the density of electrons.

Thermodynamics of the one-dimensional multicomponent Bariev model for correlated hopping

The N-component Bariev model for correlated hopping in one dimension is investigated within the framework of Bethe's ansatz. The thermodynamic Bethe ansatz equations are derived based on the string hypothesis for both, a repulsive and an attractive interaction. These equations are discussed in several limiting cases, such as the ground state, high temperature limit, and weak and strong coupling.

Jordan–Wigner fermionization of the one-dimensional Bariev model of three coupled XY chains

The Jordan-Wigner fermionization for the one-dimensional Bariev model of three coupled XY chains is formulated. The Lax operator in terms of fermion operators and the quantum R-matrix are presented explicitly. Furthermore, the graded reflection equations and their solutions are discussed.

Integrable open boundary conditions for the Bariev model of three coupled XY 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.

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 of Bethe ansatz equations as well as their corresponding energy expressions are derived.

A construction for R-matrices without difference property in the spectral parameter

A new construction is given for obtaining R-matrices which solve the McGuire–Yang–Baxter equation in such a way that the spectral parameters do not possess the difference property. A discussion of the derivation of the supersymmetric U model for correlated electrons is given in this context, such that applied chemical potential and magentic field terms can be coupled arbitrarily. As a limiting case the Bariev model is obtained.

Integrability of the one-dimensional Bariev model

We investigate the exact integrability of the one-dimensional (1D) Bariev model in the framework of the quantum inverse scattering method (QISM). Using the Jordan - Wigner transformation, the 1D Bariev model can be regarded as a coupled spin model. We construct the higher conserved currents which commute with the Hamiltonian. The explicit form of the conserved currents helps us to infer the L-operator of the 1D Bariev model. From the L-operator, we construct a transfer matrix which is a generating function of the conserved currents. We also find the corresponding R-matrix which satisfies the Yang - Baxter relation. Thus the exact integrability of the 1D Bariev model is established. The R-matrix does not have the `difference property' for the spectral parameter, as in the case of the 1D Hubbard model. We also provide the Lax representation and the fermionic formulation of the Yang - Baxter relation.