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

Hartree-Fock study of electronic ferroelectricity in the Falicov-Kimball model with ff-ff hopping

The Hartree-Fock (HF) approximation with the charge-density-wave (CDW) instability is used to study the ground-state phase diagram of the spinless Falicov-Kimball model (FKM) extended by $f$-$f$ hopping in two and three dimensions. It is shown that the HF solutions with the CDW instability reproduce perfectly the two-dimensional intermediate coupling phase diagram of the FKM model with $f$-$f$ hopping calculated recently by constrained path Monte Carlo (CPMC) method. Using this fact we have extended our HF study on cases that have been not described by CPMC, and namely, (i) the case of small values of $f$-electron hopping integrals, (ii) the case of weak Coulomb interactions and (iii) the three-dimensional case. We have found that ferroelectricity remains robust with respect to the reducing strength of coupling ($f$-electron hopping) as well as with respect to the increasing dimension of the system.Comment: 13 pages, 5 figure

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

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

Numerical study of magnetization processes in rare-earth tetraborides

We present a simple model for a description of magnetization processes in rare-earth tetraborides. The model is based on the coexistence of two subsystems, and namely, the spin subsystem described by the Ising model and the electronic subsystem described by the Falicov-Kimball model on the Shastry-Sutherland lattice (SSL). Moreover, both subsystems are coupled by the anisotropic spin-dependent interaction of the Ising type. We have found, that the switching on the spin-dependent interaction ($J_z$) between the electron and spin subsystems and taking into account the electron hopping on the nearest ($t$) and next-nearest ($t'$) lattice sites of the SSL leads to a stabilization of new magnetization plateaus. In addition, to the Ising magnetization plateau at $m^{sp}/m_s^{sp}=1/3$ we have found three new magnetization plateaus located at $m^{sp}/m_s^{sp}=1/2$, 1/5 and 1/7 of the saturated spin magnetization $m_s^{sp}$. The ground-states corresponding to magnetization plateaus have the same spin structure consisting of parallel antiferromagnetic bands separated by ferromagnetic stripes.Comment: 5 pages, 6 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

Momentum distribution of itinerant electrons in the one-dimensional Falicov-Kimball model

The momentum distribution $n_k$ of itinerant electrons in the one-dimensional Falicov-Kimball model is calculated for various ground-state phases. In particular, we examine the periodic phases with period two, three and four (that are ground-states for all Coulomb interactions) as well as the phase separated states (that are ground states for small Coulomb interactions). For all periodic phases examined the momentum distribution is a smooth function of $k$ with no sign of any discontinuity or singular behavior at the Fermi surface $k=k_F$. An unusual behavior of $n_k$ (a local maximum) is found at $k=3k_F$ for electron concentrations outside half-filling. For the phase separated ground states the momentum distribution $n_k$ exhibits discontinuity at $k=k_0 < k_F$. This behavior is interpreted in terms of a Fermi liquid.Comment: 17 pages, 6 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