Extended Falicov-Kimball model: Hartree-Fock vs DMFT approach
Konrad Jerzy Kapcia, Romuald Lemański, Marcin Jakub Zygmunt
备注：
13 pages, 7 figures; pdfReVTex class. This is the Accepted Manuscript version (author created) of an article accepted for publication in J. Phys.: Condens. Matter. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The article has been published on a gold open access basis under a CC BY 3.0 licence
发表信息：
Journal of Physics: Condensed Matter 33, 065602 (2021)
In this work, we study the extended Falicov-Kimball model at half-filling within the Hartree-Fock approach (HFA) (for various crystal lattices) and compare the results obtained with the rigorous ones derived within the dynamical mean field theory (DMFT). The model describes a system, where electrons with spin-$\downarrow$ are itinerant (with hopping amplitude $t$), whereas those with spin-$\uparrow$ are localized. The particles interact via on-site $U$ and intersite $V$ density-density Coulomb interactions. We show that the HFA description of the ground state properties of the model is equivalent to the exact DMFT solution and provides a qualitatively correct picture also for a range of small temperatures. It does capture the discontinuous transition between ordered phases at $U=2V$ for small temperatures as well as correct features of the continuous order-disorder transition. However, the HFA predicts that the discontinuous boundary ends at the isolated-critical point (of the liquid-gas type) and it does not merge with the continuous boundary. This approach cannot also describe properly a change of order of the continuous transition for large $V$ as well as various metal-insulator transitions found within the DMFT.
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 ground-state phase diagram of two-dimensional Falicov-Kimball model with nearest-neighbour and next-nearest-neighbour hoppings (characterized by t,t' constants, respectively) has been studied in perturbative regime, i.e. in the case when on-site Coulomb interaction constant U is much larger than t,t' ones. The fourth-order phase diagram exhibits a rich structure, more complicated than for the ordinary Falicov-Kimball model. Possible experimental implications of the presence of nnn term are shortly discussed.
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.
The effect of correlated hopping on the charge and heat transport is investigated for the Falicov-Kimball model. Exact solutions for the electrical and thermal conductivities and thermoelectric power are obtained within the dynamical mean field theory. The temperature dependences of the transport coefficients are analysed for particular values of correlated hopping which correspond to the significant reconstruction of the density of states and transport function. The cases with strong enhancement of thermoelectric properties are elucidated.
We consider a classical lattice gas that consists of more than one "species" of particles (like a spin-3/2 Ising model or the atomic limit of the extended Hubbard model), whose ground-state phase diagram is macroscopically degenerate. This gas is coupled component-wise and in the Falicov-Kimball-like manner to a multicomponent free-fermion gas. We show rigorously that a component-wise coupling of the classical subsystem to the quantum one orders the classical subsystem so that the macroscopic degeneracy is removed.
The spinless Falicov-Kimball model is solved exactly in the limit of infinite-dimensions on both the hypercubic and Bethe lattices. The competition between segregation, which is present for large U, and charge-density-wave order, which is prevalent at moderate U, is examined in detail. We find a rich phase diagram which displays both of these phases. The model also shows nonanalytic behavior in the charge-density-wave transition temperature when U is large enough to generate a correlation-induced gap in the single-particle density of states.
In this work, a lower bound for the ground state energy of the Falicov-Kimball model for intermediate densities is derived. The explicit derivation is important in the proof of the conjecture of segregation of the two kinds of fermions in the Falicov-Kimball model, for sufficiently large interactions. This bound is given by a bulk term, plus a term proportional to the boundary of the region devoid of classical particles. A detailed proof is presented for density n=1/2, where the coefficient 10^(-13) is obtained for the boundary term, in two dimensions. With suitable modifications the method ca…
The role of Coulomb disorder is analysed in the Anderson-Falicov-Kimball model. Phase diagrams of correlated and disordered electron systems are calculated within dynamical mean-field theory applied to the Bethe lattice, in which metal-insulator transitions led by structural and Coulomb disorders and correlation can be identified. Metallic, Mott insulator, and Anderson insulator phases, as well as the crossover between them are studied in this perspective. We show that Coulomb disorder has a relevant role in the phase-transition behavior as the system is led towards the insulator regime.
We present the exact solution of the Falicov-Kimball model after a sudden change of its interaction parameter using non-equilibrium dynamical mean-field theory. For different interaction quenches between the homogeneous metallic and insulating phases the system relaxes to a non-thermal steady state on time scales on the order of hbar/bandwidth, showing collapse and revival with an approximate period of h/interaction if the interaction is large. We discuss the reasons for this behavior and provide a statistical description of the final steady state by means of generalized Gibbs ensembles.
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 observation of charge stripe order in the doped nickelate and cuprate materials has motivated much theoretical effort to understand the underlying mechanism of the stripe phase. Numerical studies of the Hubbard model show two possibilities: (i) stripe order arises from a tendency toward phase separation and its competition with the long-range Coulomb interaction or (ii) stripe order inherently arises as a compromise between itinerancy and magnetic interactions. Here we determine the restricted phase diagrams of the two-dimensional Falicov-Kimball model and see that it displays rich behavio…
We study the electron-hole pair (or excitonic) condensation in the extended Falicov-Kimball model at finite temperatures based on the cluster mean-field-theory approach, where we make the grand canonical exact-diagonalization analysis of small clusters using the sine-square deformation function. We thus calculate the ground-state and finite-temperature phase diagrams of the model, as well as its optical conductivity and single-particle spectra, thereby clarifying how the preformed pair states appear in the strong-coupling regime of excitonic insulators. We compare our results with experiment o…
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 $V$.
An exact solution is presented for the frequency-dependent charge susceptibility of the spinless Falicov-Kimball model by using dynamical mean-field theory. We develop a nontrivial application of the Baym-Kadanoff "conserving approximation" formalism to exactly determine the frequency-dependent vertex function (which turns out to assume a particularly simple form). We show how the static and dynamic susceptibilities are decoupled in this model and how the dynamic susceptibility generically does not show any signal of the low-temperature charge-density-wave phase transition. We also examine the…
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.
Out-of-time ordered correlation functions for the localized $f$ electrons in the Falicov-Kimball model
Yukhnovskii Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine（乌克兰国家科学院尤赫诺夫斯基凝聚态物理研究所）；Department of Physics, Georgetown University（乔治城大学物理系）
The two-dimensional Falicov-Kimball (FK) model is analyzed using Monte Carlo method. In the case of concentrations of both itinerant and localized particles equal to 0.5 we determine temperature dependence of specific heat, charge density wave susceptibility and density-density correlation function. In the weak interaction regime we find a first order transition to the ordered state and anomalous temperature dependence of the correlation function. We construct the phase diagram of half-filled FK model. Also, the role of next-nearest-neighbor hopping on the phase diagram is analyzed. Lastly, we…
In the large-U limit, the Falicov-Kimball model maps onto an effective Ising model, with an order parameter described by a BCS-like mean-field theory in infinite dimensions. In the small-U limit, van Dongen and Vollhardt showed that the order parameter assumes a strange non-BCS-like shape with a sharp reduction near T approx T_c/2. Here we numerically investigate the crossover between these two regimes and qualitatively determine the order parameter for a variety of different values of U. We find the overall behavior of the order parameter as a function of temperature to be quite anomalous.
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…
We study thermodynamic properties of the two-dimensional (2D) Falicov-Kimball model in the presence of external magnetic field perpendicular to the lattice. The field is taken into account by the Peierls substitution in the hopping term. In the non-interacting case the field dependent energy spectrum forms the famous Hofstadter butterfly. Our results indicate that for arbitrary nonzero interaction strength and arbitrary magnetic field there is a gap in the energy spectrum at sufficiently low temperature. The gap vanishes with increase of temperature for weak coupling, however, it persists at h…
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…
We calculate the restricted phase diagram for the Falicov-Kimball model on a two-dimensional square lattice. We consider the limit where the conduction electron density is equal to the localized electron density, which is the limit related to the S_z=0 states of the Hubbard model. After considering over 20,000 different candidate phases (with a unit cell of 16 sites or less) and their thermodynamic mixtures, we find only about 100 stable phases in the ground-state phase diagram. We analyze these phases to describe where stripe phases occur and relate these discoveries to the physics behind str…
The Marginal Fermi Liquid (MFL) hypothesis proposed by Varma et al is derived from a consistent treatment of local spinfluctuations in the Falicov-Kimball model (FKM). Within an infinite-dimensional mean-field approach, a marginal Fermi liquid susceptibility and single-particle self-energy are obtained near half-filling, and a Fermi liquid phase is recovered sufficiently away from half-filling, in agreement with indications from experiments which probe the normal state of the cuprates as a function of doping
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…
The simplest statistical-mechanical model of crystalline formation (or alloy formation) that includes electronic degrees of freedom is solved exactly in the limit of large spatial dimensions and infinite interaction strength. The solutions contain both second-order phase transitions and first-order phase transitions (that involve phase-separation or segregation) which are likely to illustrate the basic physics behind the static charge-stripe ordering in cuprate systems. In addition, we find the spinodal-decomposition temperature satisfies an approximate scaling law.
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…
The Falicov-Kimball model is a simple quantum lattice model that describes light and heavy electrons interacting with an on-site repulsion; alternatively, it is a model of itinerant electrons and fixed nuclei. It can be seen as a simplification of the Hubbard model; by neglecting the kinetic (hopping) energy of the spin up particles, one gets the Falicov-Kimball model. We show that away from half-filling, i.e. if the sum of the densities of both kinds of particles differs from 1, the particles segregate at zero temperature and for large enough repulsion. In the language of the Hubbard model, t…
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 extended Falicov-Kimball model is analyzed exactly in the ground state at half filling in the limit of large dimensions. In the model the on-site and the intersite density-density interactions between all particles are included. We determined the model's phase diagram and found a discontinuous transition between two different charge-ordered phases. Our analytical calculations show that the ground state of the system is insulating for any nonzero values of the interaction couplings. We also show that the dynamical mean-field theory and the static broken-symmetry Hartree-Fock mean-field appr…
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…
