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

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.

Mixtures of fermionic atoms with mass imbalance in optical lattices

“…For V small (V = 0 1) the heavy atoms form the chessboard structure (see Fig. 6) in accordance with results obtained for the homogeneous case [18][19][20][21]. However, with increasing V , a connected cluster by heavy atoms occupied sites starts to form in the center of the trap.…”

“…For intermediate and strong interactions, the heavy atoms form the most homogeneous distributions and the ground states are always insulating. The most homogeneous distributions of heavy atoms also persist as ground states in the weak-coupling limit but only above a critical concentration of heavy atoms (U), while below (U) the ground sates are phase separated and metallic [18][19][20][21]. However, due to the confining potential the lattice sites become inequivalent, and thus it is of fundamental importance to analyse the interplay between the on-site Coulomb interaction and the confining potential.…”

Exact dynamical mean-field theory of the Falicov-Kimball model

“…Most of these rigorous results have already been summarized in reviews (Gruber, 1999;Gruber and Macris, 1996). In addition, a series of numerical calculations were performed in one and two dimensions (de Vries et al, 1993(de Vries et al, , 1994Freericks and Falicov, 1990;Gruber et al, 1994;Watson and Lemański, 1995). While not providing complete results for the model, the numerics do illustrate a number of important trends in the physics of the FK model.…”

Ground‐state properties of the three‐dimensional Falicov‐Kimball model

“…1a) the ground-states are the phase segregated configurations (felectrons clump together while remaining part of lattice is free of f -electrons). Since the ground-states corresponding to the segregated configurations are metallic [9] we arrive at an important conclusion, and namely, that the metallic domain that exists in the one and two dimensional FKM persists also in three dimensions. In the one dimensional case the region of stability of this metallic domain was restricted to low f -electron concentrations n f < 1/4 and small Coulomb interactions U ≤ 1 [8,9].…”

“…Since the ground-states corresponding to the segregated configurations are metallic [9] we arrive at an important conclusion, and namely, that the metallic domain that exists in the one and two dimensional FKM persists also in three dimensions. In the one dimensional case the region of stability of this metallic domain was restricted to low f -electron concentrations n f < 1/4 and small Coulomb interactions U ≤ 1 [8,9]. The numerical calculations performed in two dimensions revealed [8] that with increasing dimension the region of stability To verify this conjecture we have determined the ground-state configurations for increasing U at low f -electron concentrations on 4 × 4 × 4, 6 × 6 × 6 and 8 × 8 × 8 clusters.…”