Extended Falicov-Kimball Model Research Articles

Existence of excitonic insulator phase in the extended Falicov-Kimball model: SO(2)-invariant slave-boson approach

We re-examine the three-dimensional spinless Falicov-Kimball model with dispersive $f$ electrons at half-filling, addressing the dispute about the formation of an excitonic condensate, which is closely related to the problem of electronic ferroelectricity. To this end, we work out a slave-boson functional integral representation of the suchlike extended Falicov-Kimball model that preserves the $SO(2)\otimes U(1)^{\otimes 2}$ invariance of the action. We find a spontaneous pairing of $c$ electrons with $f$ holes, building an excitonic insulator state at low temperatures, also for the case of initially non-degenerate orbitals. This is in contrast to recent predictions of scalar slave-boson mean-field theory but corroborates previous Hartree-Fock and RPA results. Our more precise treatment of correlation effects, however, leads to a substantial reduction of the critical temperature. The different behavior of the partial densities of states in the weak and strong inter-orbital Coulomb interaction regimes supports a BCS-BEC transition scenario.

Bound state formation and the nature of the excitonic insulator phase in the extended Falicov-Kimball model

Motivated by the possibility of pressure-induced exciton condensation in intermediate-valence Tm[Se,Te] compounds, we study the Falicov-Kimball model extended by a finite $f$-hole valence bandwidth. Calculating the Frenkel-type exciton propagator we obtain excitonic bound states above a characteristic value of the local interband Coulomb attraction. Depending on the system parameters coherence between $c$ and $f$ states may be established at low temperatures, leading to an excitonic insulator phase. We find strong evidence that the excitonic insulator typifies either a BCS condensate of electron-hole pairs (weak-coupling regime) or a Bose-Einstein condensate (BEC) of preformed excitons (strong-coupling regime), which points toward a BCS-BEC transition scenario as Coulomb correlations increase.

Weak-coupling treatment of electronic (anti-)ferroelectricity in the extended Falicov-Kimball model

We study the (spinless) Falicov-Kimball model extended by a finite band width (hopping t f ) of the localized (f-) electrons in infinite dimensions in the weak-coupling limit of a small local interband Coulomb correlation U for half filling. In the case of overlapping conduction- and f-bands different kinds of ordered solutions are possible, namely charge-density wave (CDW) order, electronic ferroelectricity (EFE) and electronic antiferroelectricity (EAFE). The order parameters are calculated as a function of the model parameters and of the temperature. There is a first-order phase transition from the CDW-phase to the EFE- or EAFE-phase. The total energy is calculated to determine the thermodynamically stable solution. The quantum phase diagrams are calculated.

Slave-boson theory of the extended Falicov-Kimball model

The extended Falicov-Kimball model, with both an on-site hybridization potential and dispersive narrow band, is examined within the saddle-point approximation to the Kotliar-Ruckenstein [Phys. Rev. Lett. 57, 1362 (1986)] slave-boson theory. We first set the hybridization potential to zero and find that the phase diagram depends strongly on the orbital structure: for degenerate orbitals, a correlated-insulating state is found at sufficiently strong interaction strengths, whereas a finite orbital energy difference can lead to discontinuous valence transitions. The obtained phase diagram is very sensitive to the presence of a finite hybridization potential. As in Hartree-Fock theory, we find an enhancement of the hybridization by the interorbital Coulomb repulsion. The more precise treatment of correlation effects, however, leads to large deviations from the Hartree-Fock results. In the limit of vanishing hybridization, an excitonic insulator state is only found when the orbitals are degenerate, which restricts this phase to a much smaller parameter space than in other available mean-field theories.

Ground states of an extended Falicov-Kimball model

We present a non-perturbative study of an extended Falicov-Kimball model in one dimension. Working within the binary alloy interpretation, we include the spin of the itinerant electrons and a Hubbard interaction to model the inter-electron correlations. We derive an effective Ising model for the atomic configuration in order to show how the Hubbard term affects the stability of the phase separated states. Furthermore, we investigate the competition between the Mott insulator state of the itinerant electrons and the checkerboard phase of the spinless Falicov-Kimball model.

Competing orderings in an extended Falicov-Kimball model

We present a Hartree-Fock study of the Falicov-Kimball model extended by both on-site and non-local hybridization. We examine the interplay between excitonic effects and the charge-density wave (CDW) instability known to exist at zero hybridization. It is found that the CDW state remains stable in the presence of finite hybridization; for on-site hybridization the Coulomb interaction nevertheless strongly enhances the excitonic average above its value in the noninteracting system. In contrast, for non-local hybridization, we observe no such enhancement of the excitonic average or a spontaneous on-site hybridization potential. Instead, we find only a significant suppression of the excitonic correlations in the CDW state. A phenomenological Ginzburg-Landau analysis is also provided to understand the interplay.

ELECTRONICALLY DRIVEN FERROELECTRICITY IN THE EXTENDED FALICOV-KIMBALL MODEL

We calculate the quantum phase diagram of an extended Falicov-Kimball model in the intermediate coupling regime using a constrained path quantum Monte Carlo technique. The mixed-valence regime is dominated by a Bose-Einstein condensation of excitons with a built-in electric polarization.

Intermediate coupling theory of electronic ferroelectricity.

We calculate the quantum phase diagram of an extended Falicov-Kimball model for one- and two-dimensional systems in the intermediate coupling regime. Even though some features of the phase diagram are obtained analytically, the main results are calculated with a constrained path Monte Carlo technique. We find that this regime is dominated by a Bose-Einstein condensation of excitons with a built-in electric polarization. The inclusion of a finite hybridization between the bands removes the condensate but reinforces the ferroelectricity.

Thermodynamic Properties of the Generalized Falicov–Kimball Model

The thermodynamic properties: specific heat and magnetization are studied as a function of temperature, doping, and interlevel spacing within the two-dimensional extended Falicov–Kimball model for spinless fermions. It was recently shown that the strong coupling limit of the above model possesses electronically driven ferroelectric order. Thermodynamic quantities are calculated using the finite-temperature Lanczos method with additional phase-averaging for a system of 4 × 4 sites. Our results indicate that valence transition exists in the extended Falicov–Kimball model.

Finite-temperature properties of the generalized Falicov-Kimball model

The thermodynamic properties of the extended Falicov-Kimball model (FKM) for spinless fermions are studied as a function of temperature, doping, and interlevel spacing on the two-dimensional lattice. Thermodynamic quantities are calculated using the finite-temperature Lanczos method with additional phase averaging for a system of $4\ifmmode\times\else\texttimes\fi{}4$ sites. Changes of the thermodynamic properties are studied as the system evolves from its symmetric limit represented by the original Hubbard model to the other limiting case, which corresponds to the original FKM for spinless fermions. Our results indicate that valence transition exists in the extended Falicov-Kimball model.

On the flux phase conjecture at half-filling: An improved proof

We present a simplification of Lieb's proof of the flux phase conjecture for interacting fermion systems—such as the Hubbard model—at half-filling on a general class of graphs. The main ingredient is a procedure which transforms a class of fermionic Hamiltonians into reflection-positive form. The method can also be applied to other problems, which we briefly illustrate with two examples concerning thet−V model and an extended Falicov-Kimball model.

DYNAMICAL SYMMETRY OF A DIMER CLIFFORD MEAN-FIELD EXTENDED FALICOV-KIMBALL MODEL

In this letter, resorting to the Fermi-linearization technique, implemented for a two-site (dimer) cluster, we study the structure of dynamical symmetry which the use of Grassmann-Clifford mean-fields leads to, in the case of an extended Falicov-Kimball model. The resulting scheme to diagonalize the Hamiltonian is also discussed.

Exact solution of the extended Falicov-Kimball model in the limit of zero conduction band width

A method for solving exactly the Falicov-Kimball model in the limit of vanishing conduction band is proposed. By means of the path integral formalism, a general procedure for the evaluation of the exact n-point Green functions at a finite temperature is developed. The results obtained here represent a starting point for a perturbation expansion in the conduction electron band width.

A cluster-like approach for the valence transition in SmS compounds

The extended Falicov-Kimball model is applied to a cluster composed of three spinless ions. By one of these ions we simulate an interstitial impurity situation which often occurs in semiconducting SmS. The remaining two ions are taken as next nearest neighbours sitting on regular Sm lattice sites. For a proper choice of parameters these two ions may undergo a valence transition due to the presence of the impurity. The situation corresponding to an anionic impurity can be simulated in a similar way.

Role of approximation scheme for phase transition within extended Falicov-Kimball model

Abstract We have considered a simplified version of the extended Falicov-Kimball model. The decrease of the d-band width favours the discontinuous change of valence. However, an exactly solvable atomic limit does not exhibit an abrupt transition. This implies that the previous results seem to be an artefact coming from the approximations involved.

On the absence of purely electronic phase transition in extended Falicov-Kimball model

The Falicov-Kimball model extended by the hybridization between the localized and band electrons is considered in the approximation valid for the narrow band. The limit of infinite Coulomb repulsion G is considered. In spite of the fact that the approximation involved favour the abrupt change of the occupation number of ƒ-states we have not found any discontinuous solution. This suggests that the first order phase transition in SmS can not be considered as being or purely electronic nature.

Role of hybridization in phase transition in the Falicov-Kimball model

Abstract Extended Falicov-Kimball model has been considered for samarium-chalcogenides where, (a) f-f interactions are considered to be quite large, (b) periodicity of the system has been taken into account, (c) f-d interactions are considered within mean field approximation and (d) the unperturbed conduction bandwidth is taken to be non-zero. We observe both continuous as well as discontinuous transitions and hence conclude that “extended Falicov-Kimball model” is a suitable model which can describe both a first order transition and a suitable intermediate valence phase in Sm-chalcogenides.

Hybridization effect on the Falicov-Kimball model

The extended Falicov-Kimball model which includes the hybridization effect between the localized electron state and the conduction band is treated within the Hartree-Fock approximation at T=0 K. The occupation number n e of the conduction band is calculated as a function of the localized level. The both discontinuous and continuous changes of n e appear in a certain region of parameters. This result may correspond to the experimental facts of samarium-monochalcogenides under pressure.