Formation of charge-stripe phases in a system of spinless fermions or hardcore bosons

Abstract

We consider two strongly correlated two-component quantum systems, consisting of quantum mobile particles and classical immobile particles. The both systems are described by Falicov-Kimball-like Hamiltonians on a square lattice, extended by direct short-range interactions between the immobile particles. In the first system the mobile particles are spinless fermions while in the second one they are hardcore bosons. We construct rigorously ground-state phase diagrams of the both systems in the strong-coupling regime and at half-filling. Two main conclusions are drawn. Firstly, short-range interactions in quantum gases are sufficient for the appearance of charge stripe-ordered phases. By varying the intensity of a direct nearest-neighbor interaction between the immobile particles, the both systems can be driven from a phase-separated state (the segregated phase) to a crystalline state (the chessboard phase) and these transitions occur necessarily via charge-stripe phases: via a diagonal striped phase in the case of fermions and via vertical (horizontal) striped phases in the case of hardcore bosons. Secondly, the phase diagrams of the two systems (mobile fermions or mobile hardcore bosons) are definitely different. However, if the strongest effective interaction in the fermionic case gets frustrated gently, then the phase diagram becomes similar to that of the bosonic case.

Charge-Stripe Phases Versus a Weak Anisotropy of Nearest-Neighbor Hopping

“…In our recent paper [1] we addressed the problem of formation of static charge-stripe phases in systems of correlated quantum particles. Since an experimental evidence for the existence of striped phases in materials exhibiting high-temperature superconductivity has been gathered [2,3], one observes vigorous discussions of the problem of the stability of such phases in simple models of correlated electrons.…”

Ground-state phase diagrams of the generalized Falicov-Kimball model with Hund coupling

“…These findings were confirmed by rigorous studies. 11 The spinless FKM is simple enough to obtain controllable results for all values of the coupling constant. However, the model can deal only with charge ordered phases and it neglects magnetic properties.…”

The influence of correlated hopping on the ground‐state properties of the two‐dimensional Falicov–Kimball model

“…Recently, it has been found by Lemanski et al [5] that the FKM (the simple model in which only the kinetic energy of itinerant electrons and the Coulomb interaction between the itinerant and localized electrons are taken into account [6]) exhibits the ground state with charge stripe order. This work motivated Derzhko and Jedrzejewski [7], who examined the possibilities for stripe formation in the FKM extended by nearest-neighbor and next-nearest neighbor Ising interactions between the localized electrons. They found that this type of interaction stabilizes the charge stripes even in the half-filled band case.…”