The canonical Monte-Carlo is used to study the phase transitions from the low-temperature ordered phase to the high-temperature disordered phase in the two-dimensional Falicov-Kimball model with correlated hopping. As the low-temperature ordered phase we consider the chessboard phase, the axial striped phase and the segregated phase. It is shown that all three phases persist also at finite temperatures (up to the critical temperature $τ_c$) and that the phase transition at the critical point is of the first order for the chessboard and axial striped phase and of the second order for the segregated phase. In addition, it is found that the critical temperature is reduced with the increasing amplitude of correlated hopping $t'$ in the chessboard phase and it is strongly enhanced by $t'$ in the axial striped and segregated phase.
The insulator-metal-insulator transition caused by a flatband is analyzed within dynamical mean-field theory using the Anderson-Falicov-Kimball model. We observe quantitative disagreement between the present approach and previous results. The presence of interactions enhances delocalization.
The density matrix renormalization group method is used to examine possibilities of electronic ferroelectricity in the spinless Falicov-Kimball model. The model is studied for a wide range of parameters including weak and strong interactions as well as the symmetric and unsymmetric case. In all examined cases the $<d^{+}f>$-expectation value vanishes for vanishing hybridization $V$, indicating that the spinless Falicov-Kimball model does not allow for a ferroelectric ground state with a spontaneous polarization.
Both canonical and grand canonical phase diagrams of the one-dimensional Falicov-Kimball model (FKM) with correlated hopping are presented for several values of the model parameters. Using the method of restricted phase diagrams the system has been studied in the thermodynamic limit. As compare to the conventional FKM, the diagrams exhibit a loss of the hole-particle symmetry.
The extrapolation of small-cluster exact-diagonalization calculations is used to examine the influence of correlated hopping on valence and metal-insulator transitions in the one-dimensional Falicov-Kimball model. It is shown that the ground-state phase diagram as well as the picture of valence and metal-insulator transitions found for the conventional Falicov-Kimball model (without correlated hopping) are strongly changed when the correlated hopping term is added. The effect of correlated hopping is so strong that it can induce the insulator-metal transition, even in the half-filled band case…
The extrapolation of small-cluster exact-diagonalization calculations is used to examine the possibility of electronic ferroelectricity in the one dimensional spinless and spin-one-half Falicov-Kimball model (FKM). It is found that neither spinless nor spin-one-half version of the FKM does not allow for a ferroelectric ground state with a spontaneous polarization, i.e. there is no nonvanishing $<d^{+}f>$-expectation value for vanishing hybridization $V$.
We prove the Jonson-Mahan theorem for the thermopower of the Falicov-Kimball model by solving explicitly for the correlation functions in the large dimensional limit. We prove a similar result for the thermal conductivity. We separate the results for thermal transport into the pieces of the heat current that arise from the kinetic energy and those that arise from the potential energy. Our method of proof is specific to the Falicov-Kimball model, but illustrates the near cancellations between the kinetic-energy and potential-energy pieces of the heat current implied by the Jonson-Mahan theorem.
The ground state phase diagrams of the Falicov--Kimball model with local disorder is derived within the dynamical mean--field theory and using the geometrically averaged (''typical'') local density of states. Correlated metal, Mott insulator and Anderson insulator phases are identified. The metal--insulator transitions are found to be continuous. The interaction and disorder compete with each other stabilizing the metallic phase against occurring one of the insulators. The Mott and Anderson insulators are found to be continuously connected.
The infinite-dimensional spin one-half Falicov-Kimball model in an external magnetic field is solved exactly. We calculate the magnetic susceptibility in zero field, and the magnetization as a function of the field strength. The model shows an anomalous magnetic response from thermally excited local moments that disappear as the temperature is lowered. We describe possible real materials that may exhibit this kind of anomalous behavior.
Employing a combination of a sign-free Monte Carlo approach and nonequilibrium Green's function techniques, we study nonequilibrium charge transport in a model heterostructure, where a two-dimensional spin-less Falicov-Kimball system is coupled to two noninteracting leads. We show that the transport characteristic depends sensitively on the electrostatic potential in the system and exhibits different properties for different phases of the Falicov-Kimball model. In particular, pronounced step-like changes of the current and transmission are observed at the phase boundaries, evident even on a lo…
The spin-one-half Falicov-Kimball model is solved exactly on an infinite-coordination-number Bethe lattice in the thermodynamic limit. This model is a paradigm for a charge-transfer metal-insulator transition where the occupancy of localized and delocalized electronic orbitals rapidly changes at the metal-insulator transition (rather than the character of the electronic states changing from insulating to metallic as in a Mott-Hubbard transition). The exact solution displays both continuous and discontinuous (first-order) transitions.
In this paper we extend the Falicov-Kimball model (FKM) to the case where the "quasi-particles" entering the FKM are not "ordinary" fermions. As an example we first discuss how the FKM can be generalized to the case with spin-dependent hopping. Afterwards we discuss several cases where the "quasi-particles" entering the FKM are Majorana fermions (extended Majorana-Falicov-Kimball Model (MFKM). Two examples of extended MFKM are discussed in detail: (i) a $p$-wave BCS superconductor on a bipartite lattice and (ii) a BCS-Anderson model. We also discuss the most general forms of extended MFKM, inc…
In the Falicov-Kimball model, a model for (annealed) disorder, we expect weak localization corrections to the optical conductivity. However, we get such weak localization effects only when employing a pp-ladder approximation in the dual fermion approach. In the full parquet approach these pp-contributions are suppressed by ph-reducible diagrams. For the optical conductivity, we find that the pht-channel yields the main contribution, even in the region where weak localization in the pp-ladder was indicated.
I show that a spontaneous electric polarization is developed in the solution of the Falicov-Kimball model (FKM) by mapping the strong coupling limit of the model into an $xxz$ spin 1/2 model with a magnetic field. In this way, I can determine the phase diagram of the strongly interacting model that shows a transition to a mixed valence regime containing two phases: orbital ordering and Bose-Einstein condensation of excitons with a built in electric polarization. The results are extended to the intermeditate and weak coupling regimes.
We use a novel approach to analyze the one dimensional spinless Falicov-Kimball model. We derive a simple effective model for the occupation of the localized orbitals which clearly reveals the origin of the known ordering. Our study is extended to a quantum model with hybridization between the localized and itinerant states; we find a crossover between the well-known weak- and strong-coupling behaviour. The existence of electronic polarons at intermediate coupling is confirmed. A phase diagram is presented and discussed in detail.
The extended Falicov-Kimball model which contains hybridization between localized level and conduction band has been studied using the exact diagonalization method. We obtain the single-particle density of states and the valency from this method and analyze the behaviors of valence transition and activation gap. We find that the valence transition is continuous due to hybridization, while the activation gap closes discontinuously. Moreover, the onset of the valence transition and the closing point of the activation gap mismatch each other. Our result is well consistent with the recent experime…
Falicov and Kimball proposed a real-axis form for the free energy of the Falicov-Kimball model that was modified for the coherent potential approximation by Plischke. Brandt and Mielsch proposed an imaginary-axis form for the free energy of the dynamical mean field theory solution of the Falicov-Kimball model. It has long been known that these two formulae are numerically equal to each other; an explicit derivation showing this equivalence is presented here.
The Falicov-Kimball model has been known to phase separate when the correlation strength is large and the temperature is low. We examine the stability of phase separation under the influence of an additional electron-phonon interaction that tries to force the electron density to be homogeneous. We find that the electron-phonon interaction eventually destroys the phase-separated state once it becomes larger than some critical value. The results of this work may have an influence on theories of collossal magentoresistance materials.
We analyze the thermal transport properties of the Falicov-Kimball model concentrating on locating regions of parameter space where the thermoelectric figure-of-merit ZT is large. We focus on high temperature for power generation applications and low temperature for cooling applications. We constrain the static particles (ions) to have a fixed concentration, and vary the conduction electron concentration as in the binary-alloy picture of the Falicov-Kimball model. We find a large region of parameter space with ZT>1 at high temperature and we find a small region of parameter space with ZT>1 at …
The extrapolation of finite-cluster calculations is used to examine properties of the one-dimensional Falicov-Kimball model with correla It is shown that the correlated hopping strongly influences both the transitions and the conducting properties of the model and so it sho neglected in the correct description of materials with correlated el This is illustrated for two selected values of the Coulomb interacti that represent typical behavior of the model for small and intermedi (strong) interactions. In both cases the insulator-metal transitions (accompanied by continuous or discontinuous valen…
We propose a new, controlled approximation scheme that explicitly includes the effects of non-local correlations on the $D=\infty$ solution. In contrast to usual $D=\infty$, the selfenergy is selfconsistently coupled to two-particle correlation functions. The formalism is general, and is applied to the two-dimensional Falicov-Kimball model. Our approach possesses all the strengths of the large-D solution, and allows one to undertake a systematic study of the effects of inclusion of k-dependent effects on the $D=\infty$ picture. Results for the density of states $ρ(ω)$, and the single particle …
We derive an analytical expression for the local two-particle vertex of the Falicov-Kimball model, including its dependence on all three frequencies, the full vertex and all reducible vertices. This allows us to calculate the self energy in diagrammatic extensions of dynamical mean field theory, specifically in the dual fermion and the one-particle irreducible approach. Non-local correlations are thence included and originate here from charge density wave fluctuations. At low temperatures and in two dimensions, they lead to a larger self energy contribution at low frequencies and a more insula…
An approximate analytical scheme of the dynamical mean field theory (DMFT) is developed for the description of the electron (ion) lattice systems with Hubbard correlations within the asymmetric Hubbard model where the chemical potentials and electron transfer parameters depend on an electron spin (a sort of ions). Considering a complexity of the problem we test the approximation in the limiting case of the infinite-$U$ spinless Falicov-Kimball model. Despite the fact that the Falicov-Kimball model can be solved exactly within DMFT, the densities of states of localized particles have not been c…
Nonequilibrium dynamical mean-field theory (DMFT) is developed for the case of the charge-density-wave ordered phase. We consider the spinless Falicov-Kimball model which can be solved exactly. This strongly correlated system is then placed in an uniform external dc electric field. We present a complete derivation for nonequilibrium dynamical mean-field theory Green's functions defined on the Keldysh-Schwinger time contour. We also discuss numerical issues involved in solving the coupled equations.
We examine the one-dimensional spinless Falicov-Kimball model extended by a hybridization potential between the localized and itinerant electron states. Below half-filling we find a crossover from a mixed-valence metal to an integer-valence phase separated state with increasing on-site Coulomb repulsion. This crossover regime is characterized by local competition between the strong- and weak-coupling behaviour, manifested by the formation of an electronic polaron liquid. We identify this intermediate-coupling regime as a charge-analogy of the Griffiths phase; a phase diagram is presented and d…
We present a simple, but very realistic, model for a description of pressure induced valence and metal-insulator transitions in mixed valence systems. It is based on the extended Falicov-Kimball model and the supposition that the key interaction governing these transitions is the nonlocal hybridization between the localized $f$ and itinerant $d$ electrons. Taking into account, in addition, the~parametrization between the external pressure and the $d$-$f$ hybridization (the experimental fact), the model is able to describe, at least qualitatively, valence as well as metal-insulator transitions …
Thermodynamic properties of the spinless Falicov-Kimball model are studied on a triangular lattice using numerical diagonalization technique with Monte-Carlo simulation algorithm. Discontinuous metal-insulator transition is observed at finite temperature. Unlike the case of square lattice, here we observe that the finite temperature effect is not able to smear out the discontinuous metal-insulator transition seen in the ground state. Calculation of specific heat (C_v) shows single and double peak structures for different values of parameters like on-site correlation strength (U), f-electron en…
The spinless Falicov-Kimball model is one of the simplest models of many-body physics. While the conduction-electron density of states is temperature independent in the normal state, the f-electron density of states is strongly temperature dependent---it has an orthogonality catastrophe singularity in the metallic phase and is gapped in the insulating phase. The question we address here is whether the spectral gap is the same for both electron species as T->0. We find strong evidence to indicate that the answer is affirmative.
The two-dimensional Falicov-Kimball model in the presence of a perpendicular magnetic field is investigated by the dynamical mean-field theory. Within the model the interplay between electron correlations and the fine electron structure due to the magnetic field is essentially emerged. Without electron correlations the magnetic field induces the electron structure to the so-called Hofstadter butterfly. It is found that when electron correlations drives the metal-insulator transition, they simultaneously smear out the fine structure of the Hofstadter butterfly. In a long-range ordered phase, th…
The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory for the Anderson-Falicov-Kimball model with nearest-neighbors and next-nearest-neighbors hopping. The half-filled band is analyzed in terms of the chemical potential of the system using the geometric and arithmetic averages. We also introduce the on-site energies exhibiting a long-range correlated disorder, which generates a system with similar characteristics as the one created by a random independent variable distribution. A decrease in the correlated disorder reduces the extended ph…
We study the effects of interband hybridization within the framework of an extended Falicov-Kimball model with itinerant $c$ and $f$ electrons. An explicit interband hybridization breaks the U(1) symmetry associated with the conservation of the difference between the total number of particles in each band. As a result, the degeneracy between multipolar electric and chiral orderings is lifted. We analyze the weak- and strong-coupling limits of the $c$-$f$ electron Coulomb interaction at zero temperature, and derive the corresponding mean-field quantum phase diagrams at half-filling for a model …
We study the spin-1/2 Falicov-Kimball model with conduction and localized $f$ electrons on the Penrose lattice using the real-space dynamical mean-field theory. By changing the $f$ electron level, the $f$ electron density at each site changes continuously, in contrast to periodic systems with first-order valence transitions. In the intermediate valence regime, the local $f$ electron number strongly depends on a wider range of the Penrose structure surrounding its lattice site, in spite of the local interaction between the conduction and $f$ electrons. The temperature dependence of the magnetic…
Using the projector-based renormalization method we investigate the formation of the excitonic insulator phase in the two-dimensional (2D) spinless Falicov-Kimball model with dispersive $f$ electrons and address the existence of excitonic bound states at high temperatures on the semiconductor side of the semimetal-semiconductor transition. To this end we calculate the imaginary part of the dynamical electron-hole pair susceptibility and analyze the wave-vector and energy dependence of excitonic resonances emerging in the band gap. We thereby confirm the existence of the exciton insulator and i…
We consider a spinless extended Falicov--Kimball model at half-filling, for the case of opposite-parity bands. Within the Hartree--Fock approach, we calculate the excitation energies in the chiral phase, which is a possible mean-field solution in the presence of a hybridisation. It is shown that the chiral phase is unstable. We then briefly review the accumulated results on stability and degeneracies of the excitonic insulator phase. Based on these, we conclude that the presence of both hybridisation and narrow-band hopping is required for electronic ferroelectricity.
We study the spectral properties of charge density wave (CDW) phase of the half-filled spinless Falicov-Kimball model within the framework of the Dynamical Mean Field Theory. We present detailed results for the spectral function in the CDW phase as function of temperature and $U$. We show how the proximity of the non-fermi liquid phase affects the CDW phase, and show that there is a region in the phase diagram where we get a CDW phase without a gap in the spectral function. This is a radical deviation from the mean-field prediction where the gap is proportional to the order parameter.
We calculate the angular resolved photoemission spectrum of the Falicov-Kimball model with electronic ferroelectricity where $d$- and $f$-electrons have different hoppings. In mix-valence regimes, the presence of strong scattering processes between $d$-$f$ excitons and a hole, created by emission of an electron, leads to the formation of pseudospin polarons and novel electronic structures with bandwidth scaling with that of $d$-$f$ excitons. Especially, in the two-dimensional case, we find that flat regions exist near the bottom of the quasiparticle band in a wide range of the $d$- and $f$-lev…
A new numerical method, recently developed to study ground states of the Falicov-Kimball model (FKM), is used to examine the effects of correlated hopping on the ground-state properties of this model in two dimensions. It is shown that the ground-state phase diagram as well as the picture of metal-insulator transitions found for the conventional FKM (without correlated hopping) are strongly changed when the correlated hopping term is added. The effect of correlated hopping is so strong that it can induce the insulator-metal transition, even in the strong-coupling limit, where the ground states…
Ground state properties of spinless, extended Falicov-Kimball model (FKM) on a finite size triangular lattice with orbital magnetic field normal to the lattice are studied using numerical diagonalization and Monte-Carlo simulation methods. We show that the ground state configurations of localized electrons strongly depend on the magnetic field. Magnetic field induces a metal to insulator transition accompanied by segregated phase to an ordered regular phase except at density $n_f = 1/2$ of localized electrons. It is proposed that magnetic field can be used as a new tool to produce segregated p…
The Falicov-Kimball model with a correlated-hopping interaction is solved using an extended dynamical mean-field theory that becomes exact in the limit of large dimensions. The effect of correlated hopping is to introduce nonlocal self-energy components that retain full dynamics as D goes to infinity, thus introducing an explicit k-dependence to the single-particle self-energy. An explicit solution for the homogeneous phase at D = 2 reveals significant nonlocal dynamical contributions in the physically relevant regime of a moderately large correlated-hopping amplitude, indicating that importan…
The generalized spin-one-half Falicov-Kimball model with Hund and Hubbard coupling is used to examine effects of spin ordering on superconducting correlations in the strongly correlated electron and spin systems. It is found that the ferromagnetic spin clusters (lines, bands, domains) suppress the superconducting correlations in the d-wave chanel, while the antiferromagnetic ones have the fully opposite effect. The enhancement of the superconducting correlations due to the antiferromagnetic spin ordering is by factor 3 in the axial striped phase and even by the factor 8 in the phase segregated…
The systematic study of ground-state properties of the three-dimensional Falicov-Kimball model is performed by a well-controlled numerical method. The results obtained are used to categorize the ground-state configurations according to common features for weak, intermediate and strong interactions. It is shown that only a few configuration types form the basic structure of the phase diagram. In particular, the largest regions of stability correspond to phase segregated configurations, striped configurations and configurations in which electrons are distributed in diagonal planes with incomplet…
A combination of small-cluster exact-diagonalization calculations and a well-controlled approximative method is used to examine the ground-state phase diagrams of the spin-one-half Falicov-Kimball model extended by the spin-dependent on-site interaction ($J$) between localized spins and itinerant ($d$) electrons, as well as by external magnetic field ($h$). Both the magnetic ordering and metamagnetic transitions are analysed as functions of $h$ and the number of itinerant electrons ($N_d$) at selected $J$. Various magnetic superstructures including axial and diagonal spin stripes are observed …
The $f$ and $d$ electron density of states of the one-dimensional Falicov-Kimball model are studied in the weak-coupling limit by exact diagonalization calculations. The resultant behaviors are used to examine the $d$-electron gap ($Δ_{d}$), the $f$-electron gap ($Δ_{f}$), and the $fd$-electron gap ($Δ_{fd}$) as functions of the $f$-level energy $E_f$ and hybridization $V$. It is shown that the spinless Falicov-Kimball model behaves fully differently for zero and finite hybridization between $f$ and $d$ states. At zero hybridization the energy gaps do not coincide ($Δ_{d}\neq Δ_{f} \neq Δ_{fd}…
We explore the spontaneous formation of an excitonic insulator state at the semimetal-semiconductor transition of mixed-valence materials in the framework of the spinless Falicov-Kimball model with direct $f$-$f$ electron hopping. Adapting the projector-based renormalization method, we obtain a set of renormalization differential equations for the extended Falicov-Kimball model parameters and finally derive analytical expressions for the order parameter, as well as for the renormalized $c$- and $f$-electron dispersions, momentum distributions, and wave-vector resolved single-particle spectral …
Quantum Monte Carlo simulations reveal an exotic metallic phase with a single-particle gap but gapless spin and charge excitations and a nonsaturating resistivity in a two-dimensional SU(2) Falicov-Kimball model. An exact duality between this model and an unconstrained slave-spin theory leads to a classification of the phase as a fractionalized or orthogonal metal whose low-energy excitations have different quantum numbers than the original electrons. Whereas the fractionalized metal corresponds to the regime of disordered slave spins, the regime of ordered slave spins is a Fermi liquid. At a …
The spin-dependent Falicov-Kimball model (FKM) is studied on a triangular lattice using numerical diagonalization technique and Monte-Carlo simulation algorithm. Magnetic properties have been explored for different values of parameters: on-site Coulomb correlation $U$, exchange interaction $J$ and filling of electrons. We have found that the ground state configurations exhibit long range Neèl order, ferromagnetism or a mixture of both as $J$ is varied. The magnetic moments of itinerant ($d$) and localized ($f$) electrons are also studied. For the one-fourth filling case we found no magnetic mo…
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 transiti…
We comparatively study the excitonic insulator state in the extended Falicov-Kimball model (EFKM, a spinless two-band model) on the two-dimensional square lattice using the variational cluster approximation (VCA) and the cluster dynamical impurity approximation (CDIA). In the latter, the particle-bath sites are included in the reference cluster to take into account the particle-number fluctuations in the correlation sites. We thus calculate the particle-number distribution, order parameter, ground-state phase diagram, anomalous Green's function, and pair coherence length, thereby demonstrating…
The Falicov-Kimball model was introduced in 1969 as a statistical model for metal-insulator transitions; it includes itinerant and localized electrons that mutually interact with a local Coulomb interaction and is the simplest model of electron correlations. It can be solved exactly with dynamical mean-field theory in the limit of large spatial dimensions which provides an interesting benchmark for the physics of locally correlated systems. In this review, we develop the formalism for solving the Falicov-Kimball model from a path-integral perspective, and provide a number of expressions for si…
Metal-insulator transitions in a three-component Falicov-Kimball model are investigated within the Kotliar-Ruckenstein slave boson mean-field approach. The model describes a mixture of two interacting fermion atom species loaded into an optical lattice at ultralow temperature. One species is two-component atoms, which can hop in the optical lattice, and the other is single-component atoms, which are localized. Different correlation-driven metal-insulator transitions are observed depending on the atom filling conditions and local interactions. These metal-insulator transitions are classified by…
We calculate the total electronic Raman scattering spectrum for a system with a charge density wave on an infinite-dimensional hypercubic lattice. The problem is solved exactly for the spinless Falicov-Kimball model with dynamical mean-field theory. We include the nonresonant, mixed, and resonant contributions in three common experimental polarizations, and analyze the response functions for representative values of the energy of the incident photons. The complicated scattering response can be understood from the significant temperature dependence of the many-body density of states, and includ…
The ground-state density of states of the half-filled Falicov-Kimball model contains a charge-density-wave gap. At finite temperature, this gap is not immediately closed, but is rather filled in by subgap states. For a specific combination of parameters, this leads to a stable phase where the system is in an ordered charge-density-wave phase, but there is high density of states at the Fermi level. We show that this property can be, in finite dimensions, traced to a crossing of sharp states resulting from the single particle excitations of the localized subsystem. The analysis of the inverse pa…
We perform a perturbative analysis for the nonequilibrium Green functions of the spinless Falicov-Kimball model in the presence of an arbitrary external time-dependent but spatially uniform electric field. The conduction electron self-energy is found from a strictly truncated second-order perturbative expansion in the local electron-electron repulsion U. We examine the current at half-filling, and compare to both the semiclassical Boltzmann equation and exact numerical solutions for the contour-ordered Green functions from a transient-response formalism (in infinite dimensions) on the Kadanoff…
The exact solution for the thermodynamic and dynamic properties of the infinite-dimensional multi-component Falicov-Kimball model for arbitrary concentration of d- and f-electrons is presented. The emphasis is on a descriptive derivation of important physical quantities by the equation of motion technique. We provide a thorough discussion of the f-electron Green function and of the susceptibility to spontaneous hybridization. The solutions are used to illustrate different physical systems ranging from the high-temperature phase of the YbInCu4 family of materials to an examination of classical …
The formation and condensation of excitonic bound states of conduction-band electrons and valence-band holes surely belongs to one of the most exciting ideas of contemporary solid state physics. In this short review we present the latest progress in this field reached by the density-matrix-renormalization-group (DMRG) calculations within various extensions of the Falicov-Kimball model. Particular attention is paid to a description of crucial mechanisms (interactions) that affect the stability of the excitonic phase, and namely: (i) the interband $d$-$f$ Coulomb interaction, (ii) the $f$-electr…
We perform a simplified analysis of finite temperature properties of the generalized Falicov-Kimball model with Hund coupling. The model is studied on the square lattice for fixed values of \emph{f-electron} and \emph{d-electron} densities $ρ_f=1/2$, $ρ_d=1$. Using an approxiamte scheme we estimated free energies of the following three phases: the charge and spin ordered (SCO), the charge ordered (CO) and the non-ordered (NO). Comparing the free energies we detected phase transitions and found how the transition temperatures depend on the on-site interaction parameters. It appears, that the tr…
Based on the SO(2)-invariant slave-boson scheme, the static charge, orbital, and excitonic susceptibilities in the extended Falicov-Kimball model are calculated. Analyzing the phase without long-range order we find instabilities towards charge order, orbital order, and the excitonic insulator (EI) phase. The instability towards the EI is in agreement with the saddle-point phase diagram. We also evaluate the dynamic excitonic susceptibility, which allows the investigation of uncondensed excitons. We find qualitatively different features of the exciton dispersion at the semimetal-EI and at the s…
The f-electron spectral function of the Falicov-Kimball model is calculated within the dynamical mean-field theory using the numerical renormalization group method as the impurity solver. Both the Bethe lattice and the hypercubic lattice are considered at half filling. For small U we obtain a single-peaked f-electron spectral function, which --for zero temperature-- exhibits an algebraic (X-ray) singularity ($|ω|^{-α}$) for $ω\to 0$. The characteristic exponent $α$ depends on the Coulomb (Hubbard) correlation U. This X-ray singularity cannot be observed when using alternative (Keldysh-based) m…
The f-electron spectral function of the Falicov-Kimball model is calculated via a Keldysh-based many-body formalism originally developed by Brandt and Urbanek. We provide results for both the Bethe lattice and the hypercubic lattice at half filling. Since the numerical computations are quite sensitive to the discretization along the Kadanoff-Baym contour and to the maximum cutoff in time that is employed, we analyze the accuracy of the results using a variety of different moment sum-rules and spectral formulas. We find that the f-electron spectral function has interesting temperature dependenc…
The extrapolation of small-cluster exact-diagonalization calculations is used to study the influence of doping on valence transitions in the spinless Falicov-Kimball model at nonzero temperatures. Two types of doping are examined, and namely, the substitution of rare-earth ions by non-magnetic ions that introduce (i) one or (ii) none additional electron (per non-magnetic ion) into the conduction band. It is found that the first type of substitution increases the average $f$-state occupancy of rare-earth ions, whereas the second type of substitution has the opposite effect. The results obtained…
The spinless Falicov-Kimball model is studied by the use of a recently developed projector-based renormalization method (PRM) for many-particle Hamiltonians. The method is used to evaluate static and dynamic quantities of the one-dimensional model at half-filling. To these belong the quasiparticle excitation energy $\tildeε_k$ and the momentum distribution $n_k$ of the conduction electrons and spatial correlation functions of the localized electrons. One of the most remarkable results is the appearance of a gap in $\tildeε_k$ at the Fermi level of the order of the Coulomb repulsion $U$, which …
