Ground states of the spinless Falicov-Kimball model

Abstract

We present some exact results for the ground states of the Falicov-Kimball model outside the symmetry point. Three ion configurations have been considered: the chessboard configuration and the completely empty and the fully occupied configurations.Using a method based onTchebycheff-Markov inequalities, we determine domains in the plane of chemical potentials p, and p, "where these configurations are ground states.

Electronic structure of the Falicov-Kimball model with a magnetic field: Dynamical mean-field study

“…It is well known that away from half filling and in the ab- sence of magnetic field the localized particles form at low temperature the complex charge patterns. [25][26][27] The charge patterns may be periodic or separated depending on the model parameters. In the presence of the magnetic field the periodic charge patterns may preserve the fine structure of the Hofstadter butterfly, because there is no a superposition of the lower and upper Hubbard contributions in the local Green function, like in the checkerboard charge-ordered phase.…”

“…23,24 Much progress has been made on solving the FKM in both exact and approximation ways, where all properties of the conduction electrons are well known. [25][26][27][28] In the homogeneous phase the FKM displays a metal-insulator transition. When the Coulomb interaction is strong, it prevents the mobility of itinerant electrons by forming the Mott-Hubbard gap.…”

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

“…At the hole-particle symmetry point, the system under consideration has very special properties, which simplify studies of its phase diagram [22]. Moreover, by means of the defined above hole-particle transformations one can determine a number of symmetries of the grand-canonical phase diagram [25]. The peculiarity of the model is that the case of attraction (U < 0) and the case of repulsion (U > 0) are related by a unitary transformation (the hole-particle transformation for ions): if S = {s x } x∈Λ is a ground-state configuration at (µ e , µ i ) for U > 0, then −S = {−s x } x∈Λ is the ground-state configuration at (µ e , −µ i ) for U < 0.…”

“…Unfortunately, in contrast to the lower-order cases, the potentials (H f ermion T ) (4) and (H boson T ) (4) turn out to be the m-potentials only in a small part of (ω, δ, ε)-space. This difficulty can be overcome by introducing the so called zeropotentials [25,29,27], denoted K (4) T , that are invariant with respect to the symmetries of H 0 and satisfy the condition…”

“…In order to construct a phase diagram according to a k-th order effective Hamiltonian, we use the m-potential method introduced in [28], with technical developments described in [25,29,27]. …”