Ground state properties of the spinless Falicov-Kimball model: Crystallization and metal-insulator transitions off the hole-particle symmetry point

Jędrzejewski, Janusz; Lach, J.; Łẏwa, R.

doi:10.1016/0378-4371(89)90263-x

Cited by 28 publications

(9 citation statements)

References 7 publications

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“…We concentrate mainly on the ion subsystem, that is, we try to determine how the ions are arranged in the ground state. This sort of approach has already been used, first in [11], then in [1], [2], [3], [4],…”

Section: The Model and The Methodsmentioning

confidence: 99%

Canonical phase diagrams of the 1D Falicov-Kimball model at T = 0

Gajek¹,

Jędrzejewski²,

Lemański³

1996

Physica A: Statistical Mechanics and its Applications

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The Falicov-Kimball model of spinless quantum electrons hopping on a 1-dimensional lattice and of immobile classical ions occupying some lattice sites, with only intrasite coupling between those particles, have been studied at zero temperature by means of well-controlled numerical procedures. For selected values of the unique coupling parameter U the restricted phase diagrams (based on all the periodic configurations of localized particles (ions) with period not greater than 16 lattice constants, typically) have been constructed in the grand-canonical ensemble. Then these diagrams have been translated into the canonical ensemble. Compared to the diagrams obtained in other studies our ones contain more details, in particular they give better insight into the way the mixtures of periodic phases are formed. Our study has revealed several families of new characteristic phases like the generalized most homogeneous and the generalized crenel phases, a first example of a structural phase transition and a tendency to build up an additional symmetry -the holeparticle symmetry with respect to the ions (electrons) only, as U decreases.

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Section: The Model and The Methodsmentioning

confidence: 99%

Canonical phase diagrams of the 1D Falicov-Kimball model at T = 0

Gajek¹,

Jędrzejewski²,

Lemański³

1996

Physica A: Statistical Mechanics and its Applications

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“…by constructing restricted phase diagrams for a finite or infinite system. Initially the method of restricted phase diagrams was applied to a 2-dimensional system in [5] and to a 1-dimensional system in [6].…”

Section: Introductionmentioning

confidence: 99%

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

1994

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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 non-neutral 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 general structure of the ground states.

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“…It is also a continuation of our earlier work [5,6]. All the papers mentioned are concerned with various properties of the phase diagram of the twostate spinless Falicov-Kimball model.…”

Section: Introductionmentioning

confidence: 68%

“…'s) at zero temperature. This sort of approach has already been used by ourselves [5,6] and by Freericks and Falicov [1]. In our earlier work [5,6] a very specific set of periodic twodimensional configurations with pi = 1/2 and a sequence of pe (pe = 1/2n , n = 1, 2, ...) was considered.…”

Section: Introductionmentioning

confidence: 99%

Global Structure of the Falicov-Kimball Model Ground State Phase Diagram

1993

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The two-state spinless Falicov-Kimball model on a one-dimensional lattice is studied by means of well-controlled numericał procedures. Restricted phase diagrams in the grand-canonical ensemble and at zero temperature are constructed. The evolution of these phase diagrams, as the interaction parameter U is varied, including the band structures corresponding to configurations of localized particles (ions) and densities of mobile particles (electrons), is monitored. The changes observed enable us to draw conclusions for the global structure of the phase diagram and to make a qualitative plot of such a diagram. Particular attention is paid to the possibility of conductor-insulator transitions. The results obtained suggest that the system is an insulator for all U only if the electron and ion densities pc, p; satisfy the conditions: pe+ pi =1, 'pi -1/2|< δ < 4. For all other pairs (Pc , pi) there is a critical U at which the system undergoes a conductor-insulator transition.

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Ground state properties of the spinless Falicov-Kimball model: Crystallization and metal-insulator transitions off the hole-particle symmetry point

Cited by 28 publications

References 7 publications

Canonical phase diagrams of the 1D Falicov-Kimball model at T = 0

Canonical phase diagrams of the 1D Falicov-Kimball model at T = 0

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

Global Structure of the Falicov-Kimball Model Ground State Phase Diagram

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