Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Acta Physica Polonica A

Next-Nearest-Neighbor Hopping in the Falicov-Kimball Model

Katarzyna Czajka, Maciej M. Maśka

Published Apr 1, 2006• 0 citations
Publisher

Abstract

Results of Monte Carlo simulations for the spinless Falicov-Kimball model with the next-nearest-neighbor hopping are presented.We find the critical value of the next-nearest-neighbor hopping integral, below which the low temperature configuration of the localized particles is the same as in the presence of only the nearest-neighbor hopping.Beyond this critical value the localized particles form horizontal or vertical stripes.

DOI
10.12693/aphyspola.109.465

Related papers

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

Maciej M. Maśka, Katarzyna Czajka

The two-dimensional Falicov-Kimball (FK) model is analyzed using the 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.

arXiv:cond-mat/0504533•Physical Review B•Jul 17, 2006•76 citations

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

Maciej M. Maśka, Katarzyna Czajka

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.

•Apr 20, 2005•0 citations

One-Dimensional Falicov-Kimball Model in the Strong Coupling Limit

Pavol Farkašovský, Ivan Batko

We studied the ground state properties of the one-dimensional Falicov-Kimball model in the strong coupling limit for special periodic and aperiodic configurations of ions.The ground state phase diagrams of the model for nearest neighbor and next nearest neighbor hopping are discussed.

Acta Physica Polonica A•Feb 1, 1994•0 citations

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

Daniela Maionchi, André M. C. Souza, Hans Jürgen Herrmann +1 more

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.

arXiv:0802.2627•Physical Review B•Jun 20, 2008•4 citations

Correlated Hopping in the 1D Falicov--Kimball Model

Z. Gajek, R. Lemański

Both canonical and grand canonical phase diagrams of the one dimensional Falicov-Kimball model (FKM) with correlated hopping are presented for several values of the model parameters. Using the method of restricted phase diagrams the system has been studied in the thermodynamic limit. As compare to the conventional FKM, the diagrams exhibit a loss of the particle-hole symmetry. PACS D5.30.Fk, 71.30+h As the simplest, still non-trivial model of highly correlated electron systems, the Falicov-Kimball model (FKM) attracts growing attention among solid state physicists. It can describe variety of the most intriguing cooperative phenomena, as metal-insulator transition, mixed-valence phenomenon etc. (see e.g. the review [1]). The model deals with itinerant particles (electrons) that can hope between nearest-neighbor sites. Some of lattice sites are occupied by non-movable particles, playing a role of ions or localized electrons; we call them ”ions”. The only interaction in the system is the on-site, Coulomb-type interaction between the electrons and the ions. The interaction generates long-range correlations between the ions. The model has been investigated thoroughly in nineties. Numerous approximate results supplemented with some exact and rigorous statements reported up to now provide a good basis for further extensions of the model towards more realistic physical situations. These include the discussed here model with correlated hopping, according to which the electron hopping rate depends on occupations of relevant sites. The Hamiltonian of the FKM with correlated hopping reads:

AcPPB•Oct 1, 2001•2 citations

Thermodynamics of a spinless, extended Falicov-Kimball model on a triangular lattice

Umesh K. Yadav, Monika Dhariwal, Tulika Maitra +1 more

The exact numerical diagonalization technique with canonical Monte-Carlo algorithm is used to study the phase transitions from low temperature (ordered) phase to high temperature (disordered) phase of spinless Falicov-Kimball model on a triangular lattice with correlated hopping (t'). The low temperature (regular, striped, bounded and segregated) phases persist up to a finite critical temperature (Tc). With increasing the correlated hopping the critical temperature decreases in regular, striped and bounded phases and exotically increases in segregated phase.

AIP conference proceedings•Jan 1, 2012•0 citations
Results of Monte Carlo simulations for the spinless Falicov-Kimball model with the next-nearest-neighbor hopping are presented.We find the critical value of the next-nearest-neighbor hopping integral, below which the low temperature configuration of the localized particles is the same as in the presence of only the nearest-neighbor hopping.Beyond this critical value the localized particles form horizontal or vertical stripes.
The two-dimensional Falicov-Kimball (FK) model is analyzed using the 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.
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.
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.
Both canonical and grand canonical phase diagrams of the one dimensional Falicov-Kimball model (FKM) with correlated hopping are presented for several values of the model parameters. Using the method of restricted phase diagrams the system has been studied in the thermodynamic limit. As compare to the conventional FKM, the diagrams exhibit a loss of the particle-hole symmetry. PACS D5.30.Fk, 71.30+h As the simplest, still non-trivial model of highly correlated electron systems, the Falicov-Kimball model (FKM) attracts growing attention among solid state physicists. It can describe variety of the most intriguing cooperative phenomena, as metal-insulator transition, mixed-valence phenomenon etc. (see e.g. the review [1]). The model deals with itinerant particles (electrons) that can hope between nearest-neighbor sites. Some of lattice sites are occupied by non-movable particles, playing a role of ions or localized electrons; we call them ”ions”. The only interaction in the system is the on-site, Coulomb-type interaction between the electrons and the ions. The interaction generates long-range correlations between the ions. The model has been investigated thoroughly in nineties. Numerous approximate results supplemented with some exact and rigorous statements reported up to now provide a good basis for further extensions of the model towards more realistic physical situations. These include the discussed here model with correlated hopping, according to which the electron hopping rate depends on occupations of relevant sites. The Hamiltonian of the FKM with correlated hopping reads:
The exact numerical diagonalization technique with canonical Monte-Carlo algorithm is used to study the phase transitions from low temperature (ordered) phase to high temperature (disordered) phase of spinless Falicov-Kimball model on a triangular lattice with correlated hopping (t'). The low temperature (regular, striped, bounded and segregated) phases persist up to a finite critical temperature (Tc). With increasing the correlated hopping the critical temperature decreases in regular, striped and bounded phases and exotically increases in segregated phase.