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

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 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

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 diagram of the asymmetric Hubbard model

The ground-state phase diagram of the asymmetric Hubbard model is studied in one and two dimensions by a well-controlled numerical method. The method allows to calculate directly the probabilities of particular phases in the approximate ground-state and thus to specify the stability domains corresponding to phases with the highest probabilities. Depending on the electron filling $n$ and the magnitude of the asymmetry $t_f/t_d$ between the hopping integrals of $f$ and $d$ electrons two different scenarios in formation of ground states are observed. At low electron fillings ($n\leq 1/3$) the ground states are always phase segregated in the limit of strong asymmetry ($t_d\gg t_f$). With decreasing asymmetry the system undergoes a transition to the phase separated state and then to the homogeneous state. For electron fillings $n>1/3$ and weak Coulomb interactions the ground state is homogeneous for all values of asymmetry, while for intermediate and strong interactions the system exhibits the same sequence of phase transitions as for $n$ small. Moreover, it is shown that the segregated phase is significantly stabilized with increasing electron filling, while the separated phases disappear gradually from the ground-state phase diagrams.Comment: 10 pages, 5 figure

Phase transitions induced by correlated hopping in the Falicov-Kimball model

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 valence transitions) ind correlated hopping are observed.Comment: 11 pages, 7 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

Ferromagnetism in the one-dimensional Hubbard model with long-range electron hopping and long-range Coulomb interaction

We present a simple, but very realistic, model for a stabilization band ferromagnetism in strongly correlated electron systems. The model is based on a generalized description of electron hopping and electron interactions on a lattice within the frame of the Hubbard Hamiltonian. Instead of the usual nearest-neighbour hopping and on-site Coulomb interaction we consider the long-range electron hopping and the long-range Coulomb interaction both with exponentially decaying amplitudes. It is shown that the simultaneous presence of both long-range mechanisms leads to the stabilization of the ferromagnetic ground state for a wide range of Coulomb interactions and electron concentrations. In particular, it is found that the long-range interaction plays a crucial role in the stabilization of the ferromagnetic state for electron concentrations $n \leq 1$ , while the long-range hopping for n > 1. Thus, one of the possible explanations of the absence of ferromagnetism in the ordinary Hubbard model (with the nearest-neighbour hopping and the on-site Coulomb interaction) could be the oversimplified description of electron hopping and electron interactions on the lattice. This opens a new route towards the understanding of band ferromagnetism in strongly correlated electrons systems

The influence of nonlocal interactions on valence transitions and formation of excitonic bound states in the generalized Falicov–Kimball model

We use the density-matrix-renormalization-group (DMRG) method to study the combined effects of nonlocal interactions on valence transitions and the formation of excitonic bound states in the generalized Falicov–Kimball model. In particular, we consider the nearest-neighbour Coulomb interaction Unn between two d, two f, d and f electrons as well as the so-called correlated hopping term Uch and examine their effects on the density of conduction nd (valence nf) electrons and the excitonic momentum distribution N(q). It is shown that Unn and Uch exhibit very strong and fully different effects on valence transitions and the formation (condensation) of excitonic bound states. While the nonlocal interaction Unn suppresses the formation of zero momentum condensate (N(q = 0)) and stabilizes the intermediate valence phases with nd ~ 0.5, nf ~ 0.5, the correlated hopping term Uch significantly enhances the number of excitons in the zero-momentum condensate and suppresses the stability region of intermediate valence phases. The physically most interesting results are observed if both Unn and Uch are nonzero, when the combined effects of Unn and Uch are able to generate discontinuous changes in nf, N(q = 0) and some other ground-state quantities