Spinless Falicov-Kimball Model Research Articles

Interplay between edge states and charge density wave order in the Falicov-Kimball model on a Haldane ribbon

To determine the impact of including edge states on the phase diagram of a spinless Falicov-Kimball model on the Haldane lattice, a study of a corresponding ribbon geometry with zigzag edges is conducted. By varying the ribbon widths, the distinction between the effects connected to the mere presence of the edges and those originating from interference between the edge states is established. The local doping caused by the former is shown to give rise to a topologically trivial bulk insulator with metallic edge states. Additionally, it gives rise to a charge density wave (CDW) phase with mixed character of the subbands in various parts of the phase diagram. The impact of local doping on the CDW instability is also addressed. Two additional gapless phases are found, caused by the edges but with stability regions depending on the width of the ribbon.

Interpretable and unsupervised phase classification

Fully automated classification methods that yield direct physical insights into phase diagrams are of current interest. Here, we demonstrate an unsupervised machine learning method for phase classification which is rendered interpretable via an analytical derivation of its optimal predictions and allows for an automated construction scheme for order parameters. Based on these findings, we propose and apply an alternative, physically-motivated, data-driven scheme which relies on the difference between mean input features. This mean-based method is computationally cheap and directly interpretable. As an example, we consider the physically rich ground-state phase diagram of the spinless Falicov-Kimball model.

Magnetic field and pressure induced valence and metal-insulator transitions in the spin-one-half Falicov–Kimball model

A combination of exact diagonalization calculations and a well-controlled approximate method is used to study valence and metal-insulator transitions in the spin-one-half Falicov–Kimball model (FKM) in the external magnetic field. It is shown that there exists a critical value of the magnetic field $$h_c$$ that depends on the f-level position $$E_f$$ , above which the spin-one-half FKM maps onto the spinless FKM. In this limit the spin-one-half FKM recovers all physics of the spinless model, including the picture of valence and metal-insulator transitions induced by changes of $$E_f$$ and opens the way to its experimental verification in real systems, like rare-earth compounds in the external magnetic field. In addition, we have found that the spin-one-half FKM in the external magnetic field exhibits a wide spectrum of continuous, as well as discontinuous valence, magnetic and metal-insulator transitions that can be induced by tuning directly the external magnetic field or indirectly the external pressure (via the f-level position). The experimental verification of these transitions represent also an interesting challenge, the solution of which can shed more light on the physics of valence and metal-insulator transitions in correlated d-f electron systems. Most of presented results are calculated for the one-dimensional spin-one-half FKM, but to establish connection with the behavior of real rare-earth materials we discuss also effects of the increasing system dimension and the anisotropic spin-dependent d-f interaction, which can play an important role in these materials.

Electronic transport through correlated electron systems with nonhomogeneous charge orderings

The spinless Falicov-Kimball model exhibits outside the particle-hole symmetric point different stable nonhomogeneous charge orderings. These include the well known charge stripes and a variety of orderings with phase separated domains, which can significantly influence the charge transport through the correlated electron system. We show this by investigating a heterostructure, in which the Falicov-Kimball model on a finite two-dimensional lattice is located between two noninteracting semi-infinite leads. We use a combination of nonequilibrium Green's functions techniques with a sign-problem-free Monte Carlo method for finite temperatures or a simulated annealing technique for the ground state to address steady-state transport through the system. We show that different ground-state phases of the central system can lead to simple metallic-like or insulating charge transport characteristics, but also to more complicated current-voltage dependencies reflecting a multi-band character of the transmission function. Interestingly, with increasing temperature, the orderings tend to form transient phases before the system reaches the disordered phase. This leads to nontrivial temperature dependencies of the transmission function and charge current.

Comparison Between the f-Electron and Conduction-Electron Density of States in the Falicov-Kimball Model at Low Temperature

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.

Exciton condensation in an extended Falicov-Kimball model in the presence of orbital magnetic fields

We investigate the exciton condensation in the presence of an external, perpendicular magnetic field in a two-dimensional extended spinless Falicov-Kimball model involving itinerant and localized electrons in the half-filled limit, using self-consistent, mean-field approximations. On tuning the orbital magnetic field the excitonic averages are affected in several ways: the external field usually suppresses the excitonic average but we find that it is also possible to enhance excitonic response at some values of the magnetic field. We further examine the effect of Coulomb interaction and the f-electron hopping on the condensation of excitons for some rational values of the applied magnetic fields. The interband Coulomb interaction enhances Δ exponentially and the effect is more pronounced for low hybridization. The strength of excitonic average drops when f-electrons have a dispersion. This trend is independent of the relative sign of the c- and f-electron hopping; although the excitonic response is different for different parity of the c- and f-electrons.

Time-domain pumping a quantum-critical charge density wave ordered material

We determine the exact time-resolved photoemission spectroscopy for a nesting driven charge-density-wave (described by the spinless Falicov-Kimball model within dynamical mean-field theory). The pump-probe experiment involves two light pulses: the first is an ultrashort intense pump pulse that excites the system into nonequilibrium, and the second is a lower amplitude higher frequency probe pulse that photoexcites electrons. We examine three different cases: the strongly correlated metal, the quantum-critical charge density wave and the critical Mott insulator. Our results show that the quantum critical charge density wave has an ultra efficient relaxation channel that allows electrons to be de-excited during the pump pulse, resulting in little net excitation. In contrast, the metal and the Mott insulator show excitations that are closer to what one expects from these systems. In addition, the pump field produces spectral band narrowing, peak sharpening, and a spectral gap reduction, all of which rapidly return to their field free values after the pump is over.

Analysis of the Finite-Temperature Phase Diagram of the Spinless Falicov-Kimball Model

The finite-temperature phase diagram of the spinless Falicov–Kimball model on the Bethe lattice is analyzed using the dynamic mean field theory. Comparing the temperature-dependent density of states at various phases we detected a difference between two phases of the ordered insulator (OI-X and OI-Y) whose stability areas in the phase diagram are separated by the stability area of the ordered conductor. It appears that the difference between OI-X and OI-Y phases is due to the band inversion, consisting in a reversal of those subbands, that lie just above and below the Fermi level and are derived only from one or the other sublattice (+ or −).

Nonequilibrium Dynamical Mean-Field Theory for the Charge-Density-Wave Phase of the Falicov-Kimball Model

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.

The possibility of detection of finite temperature stripe ordering in 2D spinless Falicov–Kimball model

This paper announces a possibility of detection of finite-temperature stripe ordering in the two-dimensional Falicov–Kimball model at half-filling by extensive Monte Carlo simulations. Moreover, the tools to study orderings and to detect phase transition temperatures are presented. The use of Binder's cumulant is supplemented by finite-size magnetization profiles not analyzed previously in this context. Continuous character of phase transitions is announced. Analyses proving the existence of more complicated phases of finite-temperature stripe ordering than the checkerboard one conclude the paper.

Phase transitions in a spinless, extended Falicov–Kimball model on the triangular lattice

A numerical diagonalization technique with canonical Monte-Carlo simulation algorithm is used to study the phase transitions from low temperature (ordered) phase to high temperature (disordered) phase of spinless Falicov–Kimball model on a triangular lattice with correlated hopping (t′). It is observed that the low temperature ordered phases (i.e. regular, bounded and segregated) persist up to a finite critical temperature (Tc). In addition, we observe that the critical temperature decreases with increasing the correlated hopping in regular and bounded phases whereas it increases in the segregated phase. Single and multi peak patterns seen in the temperature dependence of specific heat (Cv) and charge susceptibility (χ) for different values of parameters like on-site Coulomb correlation strength (U), correlated hopping (t′) and filling of localized electrons (nf) are also discussed.

Phase separation in strongly correlated electron systems with wide and narrow bands: A comparison of the Hubbard-I and DMFT approximations

The spinless Falicov–Kimball model on the simple cubic lattice is analyzed in the Hubbard-I and dynamical mean field (DMFT) approximations. The Matsubara and real frequency itinerant electron Green's functions, the evolution of the system with doping, and the range of phase separation are found in two approximations. At large values of the on-site Coulomb repulsion both approximations give similar results. The phase separation can also be favorable for a more general model, where heavy electrons have a finite bandwidth. This indicates that the phase separation phenomenon is an inherent feature of the systems described by the Hubbard-like models with wide and narrow bands.

Collective excitations and stability of the excitonic phase in the extended Falicov-Kimball model

We consider the excitonic insulator state (often associated with electronic ferroelectricity), which arises on the phase diagram of an extended spinless Falicov-Kimball model (FKM) at half-filling. Within the Hartree--Fock approach, we calculate the spectrum of low-energy collective excitations in this state up to second order in the narrow-band hopping and/or hybridization. This allows to probe the mean-field stability of the excitonic insulator. The latter is found to be unstable when the case of the pure FKM (no hybridization with a fully localized band) is approached. The instability is due to the presence of another, lower-lying ground state and not to the degeneracy of the excitonic phase in the pure FKM. The excitonic phase, however, may be stabilized further away from the pure FKM limit. In this case, the low-energy excitation spectrum contains important information about the properties of the excitonic condensate (including the strongly suppressed critical temperature).

Thermodynamic studies of the two dimensional Falicov-Kimball model on a triangular lattice

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 energy (E_f) and temperature.

Phase separation and charge-ordered phases of thed=3Falicov-Kimball model at nonzero temperature: Temperature-density-chemical potential global phase diagram from renormalization-group theory

The global phase diagram of the spinless Falicov-Kimball model in d = 3 spatial dimensions is obtained by renormalization-group theory. This global phase diagram exhibits five distinct phases. Four of these phases are charge-ordered (CO) phases, in which the system forms two sublattices with different electron densities. The CO phases occur at and near half filling of the conduction electrons for the entire range of localized electron densities. The phase boundaries are second order, except for the intermediate and large interaction regimes, where a first-order phase boundary occurs in the central region of the phase diagram, resulting in phase coexistence at and near half filling of both localized and conduction electrons. These two-phase or three-phase coexistence regions are between different charge-ordered phases, between charge-ordered and disordered phases, and between dense and dilute disordered phases. The second-order phase boundaries terminate on the first-order phase transitions via critical endpoints and double critical endpoints. The first-order phase boundary is delimited by critical points. The cross-sections of the global phase diagram with respect to the chemical potentials and densities of the localized and conduction electrons, at all representative interactions strengths, hopping strengths, and temperatures, are calculated and exhibit ten distinct topologies.

Resonant Raman scattering effects in a nesting-driven charge-density-wave insulator: Exact analysis of the spinless Falicov-Kimball model with dynamical mean-field theory

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 includes a huge enhancement for photon frequencies near the charge-density-wave gap energy.

Phase transitions in the spinless Falicov-Kimball model with correlated hopping

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 $\tau_c$) 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.

Temporal response of nonequilibrium correlated electrons

In this work we examine the time-resolved, instantaneous current response for the spinless Falicov–Kimball model at half-filling, on both sides of the Mott–Hubbard metal-insulator transition, driven by a strong electric field pump pulse. The results are obtained using an exact, nonequilibrium, many-body impurity solution specifically designed to treat the out-of-equilibrium evolution of electrons in time-dependent fields. We provide a brief introduction to the method and its computational details. We find that the current develops Bloch oscillations, similar to the case of DC driving fields, with an additional amplitude modulation, characterized by beats and induced by correlation effects. Correlations primarily manifest themselves through an overall reduction in magnitude and shift in the onset time of the current response with increasing interaction strength.

Spectral signatures of the BCS-BEC crossover in the excitonic insulator phase of the extended Falicov-Kimball model

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 functions. Our numerical results proved the valence transition picture, related to the appearance of the excitonic insulator phase, in the case of overlapping $c$ and $f$ bands. Thereby the photoemission spectra show significant differences between the weak-to-intermediate and intermediate-to-strong Coulomb attraction regimes, indicating a BCS-BEC transition of the excitonic condensate.

Time-resolved photoemission of correlated electrons driven out of equilibrium

We describe the temporal evolution of the time-resolved photoemission response of the spinless Falicov-Kimball model driven out of equilibrium by strong applied fields. The model is one of the few possessing a metal-insulator transition and admitting an exact solution in the time domain. The nonequilibrium dynamics, evaluated using an extension of dynamical mean-field theory, show how the driven system differs from two common viewpoints - a quasiequilibrium system at an elevated effective temperature (the "hot" electron model) or a rapid interaction quench ("melting" of the Mott gap) - due to the rearrangement of electronic states and redistribution of spectral weight. The results demonstrate the inherent trade-off between energy and time resolution accompanying the finite width probe pulses, characteristic of those employed in pump-probe time-domain experiments, which can be used to focus attention on different aspects of the dynamics near the transition.