Crystallization and metal-insulator transition in an itinerant electron system

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

doi:10.1016/0375-9601(89)90643-9

Cited by 19 publications

(16 citation statements)

References 7 publications

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“…This is a prototype model of many-body correlations in an interacting fermion system, in which an electron gas of density ρ e interacts with a collection of heavy classical particles ("ions") of density ρ i through an on-site interaction of strength U . It has several interesting interpretations, including as a model of valence fluctuations in rare earth and transition metal oxides, as a version of the Hubbard model, and as a model of binary alloys (for background discussion, see Kennedy and Lieb 1986, Lieb 1986, Jȩdrzejewski, Lach and Lyżwa 1989a,b, Kennedy 1994, Watson and Lemański 1995, Gruber et al 1995, Gruber and Macris 1996. Let us focus on the particular case of the neutral model (ρ e = ρ i ) in the large-U limit, and on the question of determining the ground state ionic configurations, which are those for which the electrons' energy is a minimum, at fixed density.…”

Section: Introductionmentioning

confidence: 99%

Repulsive particles on a two-dimensional lattice

Watson

1997

Physica A: Statistical Mechanics and its Applications

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The problem of finding the minimum-energy configuration of particles on a lattice, subject to a generic short-ranged repulsive interaction, is studied analytically. The study is relevant to charge ordered states of interacting fermions, as described by the spinless Falicov-Kimball model. For a range of particle density including the half-filled case, it is shown that the minimum-energy states coincide with the large-U neutral ground state ionic configurations of the Falicov-Kimball model, thus providing a characterization of the latter as "most homogeneous" ionic arrangements. These obey hierarchical rules, leading to a sequence of phases described by the Farey tree. For lower densities, a new family of minimum-energy configurations is found, having the novel property that they are aperiodic even when the particle density is a rational number. In some cases there occurs local phase separation, resulting in an inherent sensitivity of the ground state to the detailed form of the interaction potential.

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Section: Introductionmentioning

confidence: 99%

Repulsive particles on a two-dimensional lattice

Watson

1997

Physica A: Statistical Mechanics and its Applications

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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: 69%

“…'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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“…are the partition function and Hamiltonian of the free phonon system respectively. Combining (5) and (8), the upper and lower bounds to the ground-state energy read…”

Section: Static Propertiesmentioning

confidence: 99%

“…There is a vast class of physical systems that may, as a first step, be modelled in terms of quantum mechanical degrees of freedom interacting with a set of classical variables. Models of this kind are used to describe for example, solvated electrons [1], metallic clusters [2], the electronic properties of polymers [3][4][5], f -and d-electron systems [6], crystallization [7,8], etc. Usually the classical environment itself displays complicated dynamical behavior and one often has to resort to a Molecular Dynamics or Monte Carlo simulation to unravel its properties.…”

Section: Introductionmentioning

confidence: 99%

Quantum molecular dynamics study of the Su-Schrieffer-Heeger model

Michielsen

Raedt

1997

Z. Phys. B

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A quantum molecular dynamics technique is presented to compute the static and dynamic properties of a system of fermions coupled to classical degrees of freedom. The method is employed to investigate the properties of the Su-Schrieffer-Heeger model, an electron-phonon model which is often used to describe the electronic properties of conjugated polymers. The Su-Schrieffer-Heeger model is shown to exhibit a metal-insulator transition away from half-filling. In the metallic phase the electron transport is collective and shows the features characteristic of Fröhlich conductivity. Our simulation data for the optical absorption at room-temperature are in good agreement with experiment.

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Crystallization and metal-insulator transition in an itinerant electron system

Cited by 19 publications

References 7 publications

Repulsive particles on a two-dimensional lattice

Repulsive particles on a two-dimensional lattice

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

Quantum molecular dynamics study of the Su-Schrieffer-Heeger model

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