Falicov-Kimball Model Research Articles

Mixtures of fermionic atoms with mass imbalance in optical lattices

Abstract We study ground-state properties of ultracold fermionic mixtures with strong mass imbalance in one and two-dimensional optical lattices through large scale numerical simulations of the attractive Falicov-Kimball model in harmonic confining potentials. In the one-dimensional case, we observe a formation of insulating atomic-density-wave domains at low particle fillings and a coexistence of insulating and metallic domains at intermediate and large particle fillings. Moreover, we show how the formation of metallic regions is reflected in the momentum distribution of the light atoms. In two dimensions, we find a rich spectrum of density-wave patterns including the homogeneous distributions, the axial striped distributions, the labyrinthine phases as well as the segregated phases.

Ground States of the Spin-One-Half Falicov-Kimball Model with Hund's Rule Coupling in Two Dimensions

The spin-one-half Falicov–Kimball model with spin-dependent on-site interaction between localized (f) and itinerant (d) electrons is studied by small-cluster exact-diagonalization calculations and a well-controlled approximative method in two dimensions. The results obtained are used to categorize the ground-state configurations according to common features (charge and spin ordering) for all f and d electron concentrations (nf and nd) on finite square lattices. It is shown that only a few configuration types form the basic structure of the charge phase diagram in the nf−nd plane. In particular, the largest regions of stability correspond to the phase segregated configurations and configurations that can be considered as mixtures of chessboard configurations and the full (empty) lattice. Since the magnetic phase diagram is much richer than the charge phase diagram, the magnetic superstructures are examined only at selected values of f and d electron concentrations.

Phase transitions in the generalized spin-one-half Falicov–Kimball model in two dimensions

The extrapolation of small-cluster exact-diagonalisation calculations and the Monte-Carlo method is used to study the spin-one-half Falicov–Kimball model extended by the spin-dependent Coulomb interaction (J) between the localized f and itinerant d electrons as well as the on-site Coulomb interaction (U ff ) between the localized f electrons. It is shown that in the symmetric case the ground-state phase diagram of the model has an extremely simple structure that consists of only two phases, and namely, the charge-density-wave (CDW) phase and the spin-density-wave (SDW) phase. The nonzero temperature studies showed that these phases persist also at finite temperatures. The critical temperature T c for a transition from the low-temperature ordered phases to the high-temperature disordered phase is calculated numerically for various values of J and U ff .

2D Falicov-Kimball Model in the Perturbative Regime at Finite Temperatures

Finite-temperature properties of the Falicov–Kimball model in two approximations were studied in the perturbative regime, i.e. for t/U ? 1, where t = 1 is the hopping constant and U = 10 denotes the Coulomb interaction strength. In our study, we determined the phase diagram of the model in the second order of the perturbation theory, where it reduces to the antiferromagnetic Ising model in the emergent magnetic field. In the fourth order, where our model constitutes the Ising model with more complicated frustrated antiferromagnetic interactions, the phase diagram was established. The Monte Carlo method was employed to investigate the phase transition lines. The existence of stripe ordering at finite temperatures is proved.

Dynamical susceptibilities of the Falicov-Kimball model with correlated hopping: general approach

The Falicov-Kimball model with correlated hopping is studied in the limit of innite spatial dimensions. Dynamical susceptibilities are calculated using the generalization of the Dynamical Mean-Field Theory (DMFT), which is based on expansion over electron hopping around the single-site limit. A special case of semi-elliptic density of states and diagonal correlated hopping is considered numerically and the absence of phase transition for all temperatures except T = 0 is demonstrated, which corresponds to the known results.

Total electronic raman scattering in the charge-density-wave phase of the spinless Falicov–Kimball model

The total electronic Raman scattering spectrum, including the nonresonant, mixed and resonant components, is determined for the charge-density-wave (CDW) phase of the spinless Falicov-Kimball model at half filling within dynamical mean-field theory. Its frequency dependence is investigated for different values of the energy of the incident photons. The spectra reflect the different structures in the density of states and how they are modified by screening and resonance effects. The calculations are performed for the $B_{\rm 1g}$, $B_{\rm 2g}$ and $A_{\rm 1g}$ symmetries (which are typically examined in experiment). Our results for the resonance effects of the Raman spectra, found by tuning the energy of the incident photons, give information about the many-body charge dynamics of the CDW-ordered phase.

Thermodynamics of the Generalized Spin-One-Half Falicov-Kimball Model in Two Dimensions

The extrapolation of small-cluster exact-diagonalization calculations and the Monte Carlo method is used to study the spin-one-half Falicov–Kimball model extended by the spin-dependent Coulomb interaction (J) between the localized f and itinerant d electrons as well as the on-site Coulomb interaction (Uff ) between the localized f electrons. It is shown that in the symmetric case the ground-state phase diagram of the model has an extremely simple structure that consists of only two phases, and namely, the charge-density-wave phase and the spin-density-wave phase. The nonzero temperature studies showed that these phases persist also at finite temperatures. The same calculations that we performed for unsymmetric case showed that charge and spin ordering can be destroyed simultaneously or consecutively.

Correlated electron systems periodically driven out of equilibrium:Floquet+DMFTformalism

We propose to combine the Floquet formalism for systems in ac fields with the dynamical mean-field theory to study correlated electron systems periodically driven out of equilibrium by external fields such as intense laser light. This approach has a virtue that we can nonperturbatively include both the correlation effects and nonlinear effects due to the driving field, which is imperative in analyzing recent experiments for photoinduced phase transitions. In solving the problem, we exploit a general theorem that the Hamiltonian in a Floquet matrix form can be exactly diagonalized for single-band noninteracting systems. As a demonstration, we have applied the method to the Falicov-Kimball model in intense ac fields to calculate the spectral function. The result shows that photoinduced midgap states emerge from strong ac fields, triggering an insulator-metal transition.

Measuring correlated electron dynamics with time-resolved photoemission spectroscopy

Time-resolved photoemission experiments can reveal fascinating quantum dynamics of correlated electrons. However, the thermalization of the electronic system is typically so fast that very short probe pulses are necessary to resolve the time evolution of the quantum state, and this leads to poor energy resolution due to the energy-time uncertainty relation. Although the photoemission intensity can be calculated from the nonequilibrium electronic Green's functions, the converse procedure is therefore difficult. We analyze a hypothetical time-resolved photoemission experiment on a correlated electronic system, described by the Falicov-Kimball model in dynamical mean-field theory, which relaxes between metallic and insulating phases. We find that the real-time Green's function which describes the transient behavior during the buildup of the metallic state cannot be determined directly from the photoemission signal. On the other hand, the characteristic collapse-and-revival oscillations of an excited Mott insulator can be observed as oscillating weight in the center of the Mott gap in the time-dependent photoemission spectrum.

Spectral properties of orbital polarons in Mott insulators

We address the spectral properties of Mott insulators with orbital degrees of freedom, and investigate cases where the orbital symmetry leads to Ising-type superexchange in the orbital sector. The paradigm of a hole propagating by its coupling to quantum fluctuations, known from the spin t-J model, then no longer applies. We find instead that when one of the two orbital flavors is immobile, as in the Falicov-Kimball model, trapped orbital polarons coexist with free hole propagation emerging from the effective three-site hopping in the regime of large on-site Coulomb interaction U. The spectral functions are found analytically in this case within the retraceable path approximation in one and two dimensions. On the contrary, when both of the orbitals are active, as in the model for t2g electrons in two dimensions, we find propagating polarons with incoherent scattering dressing the moving hole and renormalizing the quasiparticle dispersion. Here, the spectral func- tions, calculated using the self-consistent Born approximation, are anisotropic and depend on the orbital flavor. Unbiased conclusions concerning the spectral properties are established by comparing the above results for the orbital t-J models with those obtained using the variational cluster approximation or exact diagonalization for the corresponding Hubbard models. Themore » present work makes predictions concerning the essential features of photoemission spectra of certain fluorides and vanadates.« less

Theory of time-resolved optical spectroscopy on correlated electron systems

The real-time dynamics of interacting electrons out of equilibrium contains detailed microscopic information about electronically correlated materials, which can be read out with time-resolved optical spectroscopy. The reflectivity that is typically measured in pump-probe experiments is related to the nonequilibrium optical conductivity. We show how to express this quantity in terms of real-time Green's functions using dynamical mean-field theory. As an application we study the electrical response of the Falicov-Kimball model during the ultrafast buildup of the gapped phase at large interaction.

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.

Charge and magnetic order in the spin‐one‐half Falicov–Kimball model with Hund coupling in two dimensions

AbstractThe spin‐one‐half Falicov–Kimball model with spin‐dependent on‐site interaction between localized (f) and itinerant (d) electrons is studied by small‐cluster exact‐diagonalization calculations and a well‐controlled approximative method in two dimensions. The results obtained are used to categorize the ground‐state configurations according to common features (charge and spin ordering) for all f ‐ and d ‐electron concentrations (nf and nd ) on finite square lattices. It is shown that only a few configuration types form the basic structure of the charge phase diagram in the nf –nd plane. In particular, the largest regions of stability correspond to the phase segregated configurations, the axial striped configurations and configurations that can be considered as mixtures of chessboard configurations and the full (empty) lattice. Since the magnetic phase diagram is much richer than the charge phase diagram, the magnetic superstructures are examined only at selected values of f ‐ and d ‐electron concentrations. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Initial correlations in a nonequilibrium Falicov-Kimball model

The Keldysh boundary problem in a nonequilibrium Falicov-Kimball model in infinite dimensions is studied within the truncated and self-consistent perturbation theories and the dynamical mean-field theory. Within the model the system is started in equilibrium, and later a uniform electric field is turned on. The Kadanoff-Baym-Wagner equations for the nonequilibrium Green's functions are derived and numerically solved. The contributions of initial correlations are studied by monitoring the system evolution. It is found that the initial correlations are essential for establishing the full electron correlations of the system and are independent of the starting time of preparing the system in equilibrium. By examining the contributions of the initial correlations to the electric current and the double occupation, we find that the contributions are small in relation to the total value of those physical quantities when the interaction is weak, and significantly increase when the interaction is strong. The neglect of initial correlations may cause artifacts in the nonequilibrium properties of the system, especially in the strong-interaction case.

F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach

We derive an alternative representation for the $f$-electron spectral function of the Falicov-Kimball model from the original one proposed by Brandt and Urbanek. In the new representation, all calculations are restricted to the real time axis, allowing us to go to arbitrarily low temperatures. The general formula for the retarded Green's function involves two determinants of continuous matrix operators that have the Toeplitz form. By employing the Wiener-Hopf sum equation approach and Szeg\"o's theorem, we can derive exact analytic formulas for the large-time limits of the Green's function; we illustrate this for cases when the logarithm of characteristic function (which defines the continuous Toeplitz matrix) does and does not wind around the origin. We show how accurate these asymptotic formulas are to the exact solutions found from extrapolating matrix calculations to the zero discretization size limit.

Ground-state phase diagrams of the generalized Falicov-Kimball model with Hund coupling

Charge and spin orderings are studied on the simplest one-dimensional (1D) and the two-dimensional (2D) square lattices within the generalized Falicov-Kimball model with Hund coupling between localized and itinerant electrons. Using the restricted phase diagram method (RPDM), a number of simple rules of formation of various sorts of ground-state phases have been detected. In particular, relationships between density of current carriers (electrons or holes) and type of charge and magnetic arrangement have been determined. In two dimensions in the mixed-valence regime, only axial stripes (vertical or horizontal) have been found for intermediate values of the coupling constants. They are composed of ferromagnetic or antiferromagnetic chains interchanged with nonmagnetic ones. For band fillings close to the half filling, stripe phases oriented along one of the main diagonal direction are formed. The results suggest the possibility of tuning modulations of charge and magnetic superstructures with a change in doping.

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.

THE INFLUENCE OF NONLOCAL COULOMB INTERACTION ON GROUND-STATE PROPERTIES OF THE FALICOV–KIMBALL MODEL IN ONE AND TWO DIMENSIONS

A combination of small-cluster exact diagonalizations and a well-controlled approximative method is used to study the ground states of the Falicov–Kimball model extended by nonlocal Coulomb interaction (Unon). 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 are strongly changed when the nonlocal Coulomb interaction is added. This is illustrated for three selected values of the on-site Coulomb interaction (U) that represent typical behaviors of the model for small, intermediate and strong interactions. A number of remarkable results are found: (i) the phase separation takes place for a wide range of Unonin all three interaction limits; (ii) in the weak and intermediate coupling limit, the model exhibits the nonlocal Coulomb interaction–induced insulator–metal transition; (iii) depending on the value of Unon, the model is able to describe both the continuous and the discontinuous changes of the f-electron occupation number; (iv) new types of inhomogeneous charge ordering (including various types of axial and diagonal stripes) are observed for nonzero Unon.

Anderson localization on Falicov-Kimball model with next-nearest-neighbor hopping and long-range correlated disorder

The phase diagram of correlated disordered electron systems is calculated within dynamical mean-field theory for the Anderson-Falicov-Kimball model with nearest-neighbor and next-nearest-neighbor hoppings. 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 phase.

Phase diagram of the Anderson-Falicov-Kimball model at half filling

We study the Falicov-Kimball model [Phys. Rev. Lett. 22, 997 (1969)] at half-filling in the presence of on-site disorder. Using dynamical mean-field theory, we evaluate densities of states appropriately averaged over a continuous distribution of local energies, identifying the phases that appear upon varying the Coulomb interaction and disorder strength. We focus on the existence and stability of the chessboard ordered state, including it in the complete phase diagram.