Ground-states of the three-dimensional Falicov-Kimball model

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 incomplete chessboard structure. Near half-filling, mixtures of two phases with complete and incomplete chessboard structure are determined. The relevance of these results for a description of real material is discussed.Comment: 9 pages, 4 figure

The spectral properties of the Falicov-Kimball model in the weak-coupling limit

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 ($\Delta_{d}$), the $f$-electron gap ($\Delta_{f}$), and the $fd$-electron gap ($\Delta_{fd}$) 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 ($\Delta_{d}\neq \Delta_{f} \neq \Delta_{fd}$), and the activation gap $\Delta_{fd}$ vanishes discontinuously at some critical value of the $f$-level energy $E_{fc}$. On the other hand, at finite hybridization all energy gaps coincide and vanish continuously at the insulator-metal transition point $E_f=E_{fc}$. The importance of these results for a description of real materials is discussed.Comment: 10 pages, 7 figures, LaTe

Ground-state properties of fermionic mixtures with mass imbalance in optical lattices

Ground-state properties of fermionic mixtures confined in a one-dimensional optical lattice are studied numerically within the spinless Falicov-Kimball model with a harmonic trap. A number of remarkable results are found. (i) At low particle filling the system exhibits the phase separation with heavy atoms in the center of the trap and light atoms in the surrounding regions. (ii) Mott-insulating phases always coexist with metallic phases. (iii) Atomic-density waves are observed in the insulating regions for all particle fillings near half-filled lattice case. (iv) The variance of the local density exhibits the universal behavior (independent of the particle filling, the Coulomb interaction and the strength of a confining potential) over the whole region of the local density values.Comment: 10 pages, 5 figure

The influence of long-range hopping on ferromagnetism in the Hubbard model

The phase diagram of the Hubbard model in an external magnetic field is examined by extrapolation of small-cluster exact-diagonalization calculations. Using a general expression for the hopping matrix elements ($t_{ij}\sim q^{|i-j|}$) the influence of long-range hopping (band asymmetry) on ferromagnetism in this model is studied. It is found that the long-range hopping (nonzero $q$) stabilizes ferromagnetism in an external magnetic field for $n > 1$. In the opposite limit $n \leq 1$ the fully polarized ferromagnetic state is generally suppressed with increasing $q$. The critical value of magnetic field $h$ below which the ferromagnetic state becomes unstable is calculated numerically.Comment: 8 pages, 3 Postscript figures, Late

Falicov-Kimball model and the problem of electronic ferroelectricity

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 $$-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.Comment: 9 pages, 4 figures, LaTe

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.Comment: 17 pages, 6 figure

Thermodynamics of the two-dimensional Falicov-Kimball model: a classical Monte Carlo study

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 discuss the density of states and the spectral functions for the mobile particles in weak and strong interaction regime.Comment: 15 pages, RevTe

Anomalous magnetic response of the spin-one-half Falicov-Kimball model

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.Comment: 17 pages, 6 encapsulated postscript figures (included), submitted to Phys. Rev.

Influence of Hybridization on the Properties of the Spinless Falicov-Kimball Model

Without a hybridization between the localized f- and the conduction (c-) electron states the spinless Falicov-Kimball model (FKM) is exactly solvable in the limit of high spatial dimension, as first shown by Brandt and Mielsch. Here I show that at least for sufficiently small c-f-interaction this exact inhomogeneous ground state is also obtained in Hartree-Fock approximation. With hybridization the model is no longer exactly solvable, but the approximation yields that the inhomogeneous charge-density wave (CDW) ground state remains stable also for finite hybridization V smaller than a critical hybridization V_c, above which no inhomogeneous CDW solution but only a homogeneous solution is obtained. The spinless FKM does not allow for a ''ferroelectric'' ground state with a spontaneous polarization, i.e. there is no nonvanishing $$-expectation value in the limit of vanishing hybridization.Comment: 7 pages, 6 figure

Spectral functions of the Falicov-Kimball model with electronic ferroelectricity

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 $f$-level energy difference.Comment: 5 pages, 5 figure