Molecule formation and the Farey tree in the one-dimensional Falicov-Kimball model

@article{Gruber1993MoleculeFA,
  title={Molecule formation and the Farey tree in the one-dimensional Falicov-Kimball model},
  author={Ch. Gruber and Daniel Ueltschi and Janusz Jȩdrzejewski},
  journal={Journal of Statistical Physics},
  year={1993},
  volume={76},
  pages={125-157}
}
The ground-state configurations of the one-dimensional Falicov-Kimball model are studied exactly with numerical calculations revealing unexpected effects for small interaction strength. In neutral systems we observe molecular formation, phase separation, and changes in the conducting properties; while in nonneutral systems the phase diagram exhibits Farey tree order (Aubry sequence) and a devil's staircase structure. Conjectures are presented for the boundary of the segregated domain and the… 
Ground-states of the three-dimensional Falicov-Kimball model
Abstract.A systematic study of ground-state properties of the three-dimensional Falicov-Kimball model is performed by a well-controlled numerical method. The results obtained are used to categorize
The ground-state phase diagram of the two-dimensional Falicov-Kimball model
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
Ground-state properties of the three-dimensional Falicov-Kimball model
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
A complete devil's staircase in the Falicov - Kimball model
We consider the neutral, one-dimensional Falicov - Kimball model at zero temperature in the limit of a large electron - ion attractive potential, U. By calculating the general n-ion interaction terms
New phases and structural phase transitions in the 1-D Falicov-Kimball model at T=0
Abstract The Falicov-Kimball model of spinless itinerant fermions and localized classical ions, on a one-dimensional lattice and at zero temperature, has been studied by means of restricted phase
Phase Diagram of the Two-dimensional t–t′ Falicov-Kimball Model
The ground-state phase diagram of the two-dimensional Falicov-Kimball model with nearest-neighbour and next-nearest-neighbour hoppings has been studied in the perturbative regime where hoppings are
Thermodynamics of the two-dimensional Falicov-Kimball model: a classical Monte Carlo study
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
MOMENTUM DISTRIBUTION OF ITINERANT ELECTRONS IN THE ONE-DIMENSIONAL FALICOV–KIMBALL MODEL
The momentum distribution nk 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
Charge Order in the Falicov-Kimball Model
We examine the spinless one-dimensional Falicov-Kimball model (FKM) below half-filling, addressing both the binary alloy and valence transition interpretations of the model. Using a non-perturbative
Electronic phase transitions in the spinless falicov-kimball model with correlated hopping
Abstract The extrapolation of small-cluster exact-diagonalization calculations is used to examine the influence of correlated hopping on valence and metal-insulator transitions in the one-dimensional
...
1
2
3
4
...

References

SHOWING 1-10 OF 36 REFERENCES
Ground-state phase diagram of the Falicov-Kimball model.
The two-state spinless Falicov-Kimball model on a one-dimensional lattice is studied by means of well-controlled numerical procedures. Restricted phase diagrams in the grand-canonical ensemble and at
Segregation in the Falicov-Kimball model
The ground state of the one-dimensional Falicov-Kimball model (1969) is considered for large values of the interaction strength U. If the ion density rho i=p/q (p and q relatively prime) is rational
Phase separation in the spinless Falicov-Kimball model
We discuss a one-dimensional Falicov-Kimball model away from the symmetry point of the densities by exact methods. We found the well-expected phase separation (segregation) and calculated the
Modulated phases in the Falicov-Kimball model
The arrangement of localized f electrons in the ground state of the Falicov-Kimball model is studied as a function of the energy of the f-level. For the half-filled case in one dimension,
Ground-State Energy and Low-Temperature Behavior of the One-Dimensional Falicov-Kimball Model
We consider the Falicov-Kimball model in the case of an equal number of classical "nuclei" and quantum "electrons" with Fermi statistics. In one dimension we find an exact formula for the leading
Ground state properties of a spinless Falicov-Kimball model; additional features
We have studied some energetic and structural ground state properties of a spinless Falicov-Kimball model. Using a method based on “Tchebycheff-Markoff inequalities”, we have calculated sharp upper
Ground states of the spinless Falicov-Kimball model. II
TLDR
A number of general properties of the phase diagram are obtained and an expansion for large values of the coupling constant is derived, from which results concerning particular states are deduced.
Ground states of the spinless Falicov-Kimball model
In this paper we continue our investigation of the ground states of the spinless Falicov-Kimball model in the plane of chemical potentials of the two sorts of particles involved. We obtain a number
Exact results for the distribution of thef-level ground state occupation in the spinless Falicov-Kimball model
We present sharp upper and lower bounds for the ground state energy of the spinless Falicov-Kimball model, leading to rigorous results for a special choice of parameters. In this ‘symmetric’ case we
Exact results for the spinless Falicov-Kimball model on a one-dimensional lattice
Abstract Exact explicit expressions for the density of states, density of electrons and resulting total energy of the spinless Falicov-Kimball model on a one-dimensional lattice are presented. The
...
1
2
3
4
...