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Physical review. B, Condensed matter

Ground states of the spinless Falicov-Kimball model

C. Gruber, J. Iwański, Janusz Jędrzejewski, Pirmin Lemberger

Published Feb 1, 1990• 40 citations
Publisher

Abstract

We present some exact results for the ground states of the Falicov-Kimball model outside the symmetry point. Three ion configurations have been considered: the chessboard configuration and the completely empty and the fully occupied configurations. Using a method based on Tchebycheff-Markov inequalities, we determine domains in the plane of chemical potentials ${\ensuremath{\mu}}_{e}$ and ${\ensuremath{\mu}}_{i}$, where these configurations are ground states.

DOI
10.1103/physrevb.41.2198

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physica status solidi (b)•Mar 1, 2003•6 citations
We present some exact results for the ground states of the Falicov-Kimball model outside the symmetry point. Three ion configurations have been considered: the chessboard configuration and the completely empty and the fully occupied configurations. Using a method based on Tchebycheff-Markov inequalities, we determine domains in the plane of chemical potentials \ensuremathμe{\ensuremath{\mu}}_{e}\ensuremathμe​ and \ensuremathμi{\ensuremath{\mu}}_{i}\ensuremathμi​, where these configurations are ground states.
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.
Abstract The ground‐state properties of the three‐dimensional spinless Falicov‐Kimball model are studied by a wellcontrolled 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. In addition, the picture of metal‐insulator transitions is presented. The relevance of these results for a description of real material is discussed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Two-dimensional spinless Falicov-Kimball model (FKM) with correlated hopping is studied perturbatively in the limit of large on-site Coulomb interaction U. In the half filled case (i.e., ${\ensuremath{\rho}}_{i}+{\ensuremath{\rho}}_{e}=1,$ where ${\ensuremath{\rho}}_{i},{\ensuremath{\rho}}_{e}$ are densities of ions and electrons, respectively) the effective Hamiltonian in spin variables is derived up to terms proportional to ${U}^{\ensuremath{-}3}.$ Unlike the simplest FKM case, it contains odd parity terms (resulting from the correlated hopping) in addition to even parity ones. The ground-state phase diagram of the effective Hamiltonian is examined in the (a/t,h)(a/t,h)(a/t,h) plane, where a/ta/ta/t is a parameter characterizing strength of the correlated hopping and h is a difference of chemical potentials of two sorts of particles present in the system. It appears to be asymmetric with respect to the change $\stackrel{\ensuremath{\rightarrow}}{h}\ensuremath{-}h$ and an additional ordered phase is found for a certain interval of a/t.a/t.a/t.
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 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.