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

Ground state properties of the neutral two-dimensional Falicov-Kimball model

Karl Haller

Published Jan 1, 1998• 1 citation
OpenAlex

Abstract

We focus on the two-dimensional Falicov-Kimball model in the neutral case with U >> 0. We determine the ground state ion configurations for all rational densities in (1/3, 2/5), as well as densities 1/6 and 2/11. We also determine the ground states for a sequence of densities starting at 1/5 and converging to 0. On the interval (1/3, 2/5) we show that the ground states are periodic, having the same structure as the one-dimensional ground states. For densities between 1/6 and 2/11 we show that the ground states exhibit a phase separation.

Related papers

The ground-state phase diagram of the two-dimensional Falicov-Kimball model

G I Watson, R. Lemański

The spinless Falicov-Kimball model on a two-dimensional square lattice is studied using the method of restricted phase diagrams constructed in the grand canonical ensemble. The results are compared with the one-dimensional model. Although the two-dimensional phase diagrams are more complex, with several distinct families of ion configurations occurring as ground states, there are surprising similarities with the one-dimensional case. Within each family of configurations, the ground states form a devil`s staircase structure and the configurations are constructed according to a composition rule identical to that in one dimension. It is also found that, as in one dimension, segregation occurs in the non-neutral model for large ion-electron interaction strength. Some features of the phase diagrams are understood by examining the effective two-body ion interaction.

Journal of Physics Condensed Matter•Dec 4, 1995•41 citations

Ground states of the spinless Falicov-Kimball model in the strong-coupling limit

Pavol Farkašovský, Ivan Batko

The authors have studied energetic and structural ground-state properties of the one-dimensional Falicov-Kimball model in the strong-coupling limit. Using standard perturbation theory they recover some results already obtained (the phase segregation at large interactions) and present some new results concerning the ground state, e.,g., the analytic expression for the boundary, below which the segregated configuration cannot be the ground state, and the phase diagram of the model calculated for special periodic (aperiodic) configurations of ions and for the case when the ion concentration goes to zero.

Journal of Physics Condensed Matter•Sep 20, 1993•8 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

Phase separation in the binary-alloy problem: The one-dimensional spinless Falicov-Kimball model

James K. Freericks, C. Gruber, Nicolas Macris

The ground states of the one-dimensional Falicov-Kimball model are investigated in the small-coupling limit, using nearly degenerate perturbation theory. For rational electron and ion densities, respectively, equal to p/q, ${\mathit{p}}_{\mathit{i}}$/q, with p relatively prime to q and ${\mathit{p}}_{\mathit{i}}$/q close enough to 1/2, we find that in the ground state the ion configuration has a period q. The situation is analogous to the Peierls instability, where the usual arguments predict a period-q state that produces a gap at the Fermi level and is insulating. However for ${\mathit{p}}_{\mathit{i}}$/q far enough from 1/2, this phase becomes unstable against phase separation. The ground state is a mixture of a period-q ionic configuration and an empty (or full) configuration, where both configurations have the same electron density to leading order. Combining these results with those previously obtained for strong coupling, it follows that a phase transition occurs in the ground state, as a function of the coupling, for ion densities far enough from 1/2. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9602042•Physical review. B, Condensed matter•Jun 15, 1996•22 citations

Ground States and Flux Configurations of the Two-dimensional Falicov-Kimball Model

C. Gruber, Nicolas Macris, Alain Messager +1 more

The Falicov-Kimball model is a lattice model of itinerant spinless fermions ("electrons") interacting by an on-site potential with classical particles ("ions"). We continue the investigations of the crystalline ground states that appear for various filling of electrons and ions, for large coupling. We investigate the model for square as well as triangular lattices. New ground states are found and the effects of a magnetic flux on the structure of the phase diagram is studied. The flux phase problem where one has to find the optimal flux configurations and the nuclei configurations is also solved in some cases. Finaly we consider a model where the fermions are replaced by hard-core bosons. This model also has crystalline ground states. Therefore their existence does not require the Pauli principle, but only the on-site hard-core constraint for the itinerant particles.

arXiv:cond-mat/9511092•Nov 20, 1995•0 citations

PHASE DIAGRAM OF THE FALICOV-KIMBALL MODEL WITH INFINITE-RANGE HOPPING

Pavol Farkašovský

We have studied the ground state properties of the Falicov-Kimball model with unconstrained hopping. It is shown that the model still behaves non-trivially, although it no longer depends on the actual lattice structure and dimensionality of the system. For arbitrary ion configurations with total number of ions Ni, we have been able to determine domains in the plane of the chemical potentials of electrons and ions where these ion configurations are ground states. The phase diagram of the model is discussed.

Modern Physics Letters B•Jun 10, 1992•3 citations
We focus on the two-dimensional Falicov-Kimball model in the neutral case with U >> 0. We determine the ground state ion configurations for all rational densities in (1/3, 2/5), as well as densities 1/6 and 2/11. We also determine the ground states for a sequence of densities starting at 1/5 and converging to 0. On the interval (1/3, 2/5) we show that the ground states are periodic, having the same structure as the one-dimensional ground states. For densities between 1/6 and 2/11 we show that the ground states exhibit a phase separation.
The spinless Falicov-Kimball model on a two-dimensional square lattice is studied using the method of restricted phase diagrams constructed in the grand canonical ensemble. The results are compared with the one-dimensional model. Although the two-dimensional phase diagrams are more complex, with several distinct families of ion configurations occurring as ground states, there are surprising similarities with the one-dimensional case. Within each family of configurations, the ground states form a devil`s staircase structure and the configurations are constructed according to a composition rule identical to that in one dimension. It is also found that, as in one dimension, segregation occurs in the non-neutral model for large ion-electron interaction strength. Some features of the phase diagrams are understood by examining the effective two-body ion interaction.
The authors have studied energetic and structural ground-state properties of the one-dimensional Falicov-Kimball model in the strong-coupling limit. Using standard perturbation theory they recover some results already obtained (the phase segregation at large interactions) and present some new results concerning the ground state, e.,g., the analytic expression for the boundary, below which the segregated configuration cannot be the ground state, and the phase diagram of the model calculated for special periodic (aperiodic) configurations of ions and for the case when the ion concentration goes to zero.
The ground states of the one-dimensional Falicov-Kimball model are investigated in the small-coupling limit, using nearly degenerate perturbation theory. For rational electron and ion densities, respectively, equal to p/q, pi{\mathit{p}}_{\mathit{i}}pi​/q, with p relatively prime to q and pi{\mathit{p}}_{\mathit{i}}pi​/q close enough to 1/2, we find that in the ground state the ion configuration has a period q. The situation is analogous to the Peierls instability, where the usual arguments predict a period-q state that produces a gap at the Fermi level and is insulating. However for pi{\mathit{p}}_{\mathit{i}}pi​/q far enough from 1/2, this phase becomes unstable against phase separation. The ground state is a mixture of a period-q ionic configuration and an empty (or full) configuration, where both configurations have the same electron density to leading order. Combining these results with those previously obtained for strong coupling, it follows that a phase transition occurs in the ground state, as a function of the coupling, for ion densities far enough from 1/2. \textcopyright{} 1996 The American Physical Society.
The Falicov-Kimball model is a lattice model of itinerant spinless fermions ("electrons") interacting by an on-site potential with classical particles ("ions"). We continue the investigations of the crystalline ground states that appear for various filling of electrons and ions, for large coupling. We investigate the model for square as well as triangular lattices. New ground states are found and the effects of a magnetic flux on the structure of the phase diagram is studied. The flux phase problem where one has to find the optimal flux configurations and the nuclei configurations is also solved in some cases. Finaly we consider a model where the fermions are replaced by hard-core bosons. This model also has crystalline ground states. Therefore their existence does not require the Pauli principle, but only the on-site hard-core constraint for the itinerant particles.
We have studied the ground state properties of the Falicov-Kimball model with unconstrained hopping. It is shown that the model still behaves non-trivially, although it no longer depends on the actual lattice structure and dimensionality of the system. For arbitrary ion configurations with total number of ions Ni, we have been able to determine domains in the plane of the chemical potentials of electrons and ions where these ion configurations are ground states. The phase diagram of the model is discussed.