24 research outputs found
Hartree-Fock study of electronic ferroelectricity in the Falicov-Kimball model with - 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 - 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 - 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 -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 (-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 () between the electron
and spin subsystems and taking into account the electron hopping on the nearest
() and next-nearest () lattice sites of the SSL leads to a stabilization
of new magnetization plateaus. In addition, to the Ising magnetization plateau
at we have found three new magnetization plateaus located
at , 1/5 and 1/7 of the saturated spin magnetization
. 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 and 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
-electron gap (), the -electron gap (), and the
-electron gap () as functions of the -level energy
and hybridization . It is shown that the spinless Falicov-Kimball model
behaves fully differently for zero and finite hybridization between and
states. At zero hybridization the energy gaps do not coincide (), and the activation gap vanishes
discontinuously at some critical value of the -level energy . On the
other hand, at finite hybridization all energy gaps coincide and vanish
continuously at the insulator-metal transition point . 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 () the influence of long-range hopping (band asymmetry) on
ferromagnetism in this model is studied. It is found that the long-range
hopping (nonzero ) stabilizes ferromagnetism in an external magnetic field
for . In the opposite limit the fully polarized ferromagnetic
state is generally suppressed with increasing . The critical value of
magnetic field 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 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
with no sign of any discontinuity or singular behavior at the Fermi surface
. An unusual behavior of (a local maximum) is found at
for electron concentrations outside half-filling. For the phase separated
ground states the momentum distribution exhibits discontinuity at . 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 and the
magnitude of the asymmetry between the hopping integrals of and
electrons two different scenarios in formation of ground states are
observed. At low electron fillings () the ground states are always
phase segregated in the limit of strong asymmetry (). With
decreasing asymmetry the system undergoes a transition to the phase separated
state and then to the homogeneous state. For electron fillings 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 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 , 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 , 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