Molecule Formation and the Farey Tree in the One-Dimensional Falicov-Kimball Model
C. Gruber, D. Ueltschi, J. J\c{e}drzejewski
TL;DR
This paper provides an exact analysis of the ground states in the one-dimensional Falicov-Kimball model, revealing molecular formation, phase separation, and complex Farey tree order structures in the phase diagram.
Contribution
It introduces new insights into the ground state configurations, including the Farey tree order and devil's staircase phenomena, supported by numerical calculations.
Findings
Molecular formation observed in neutral systems
Phase separation and conducting property changes
Farey sequence and devil's staircase structures in phase diagram
Abstract
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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