An extended Falicov-Kimball model on a triangular lattice

Abstract

The combined effect of frustration and correlation in electrons is a matter of considerable interest lately. In this context a Falicov-Kimball model on a triangular lattice with two localized states, relevant for certain correlated systems, is considered. Making use of the local symmetries of the model, our numerical study reveals a number of orbital ordered ground states, tuned by the small changes in parameters while quantum fluctuations between the localized and extended states produce homogeneous mixed valence. The inversion symmetry of the Hamiltonian is broken by most of these ordered states leading to orbitally driven ferroelectricity. We demonstrate that there is no spontaneous symmetry breaking when the ground state is inhomogeneous. The study could be relevant for frustrated systems like GdI2, NaTiO2 (in its low-temperature C2/m phase) where two Mott localized states couple to a conduction band.

Effect of super-exchange interaction on ground state magnetic properties of spin-dependent Falicov-Kimball model on a triangular lattice

“…The eigenvalue spectrum of the FKM Hamiltonian is obtained by numerical diagonalization technique on a finite-size triangular lattice with periodic boundary conditions (PBC). In order to calculate the average values of the physical quantities the classical Monte-Carlo simulation algorithm is employed by 'annealing' over a subset of configurations of the 'classical' variables {ω iσ = f † iσ f iσ } [5,6,7,8].…”

The nature of itineracy in CoV2O4: a first-principles study

“…where the a 1g state is localized and fully occupied by one electron and the doubly degenerate e ′ g states are itinerant and half filled by one electron [27]. Here d † iα , d iα are, respectively, the creation and annihilation operators for itinerant e ′ g electrons and f † i , f i are the same for localized a 1g electrons.…”

Metal-Insulator Transition and Band Magnetism in the Spin-$1/2$ Falicov-Kimball Model on A Triangular Lattice with External Magnetic Field

“…It is shown that these systems may very well be described by different variants of the Falicov-Kimball model (FKM) [15,16,23,24,25,26,27,11] on the triangular lattice. The FKM (having two kinds of states namely itinerant states and localized states) was originally introduced to study the metal-insulator transition in the rare-earth and transition-metal compounds [28,29].…”

“…Many numerical and exact calculations are available for the different extensions of spinless FKM on the bipartite and non-bipatatite lattices in the absence of magnetic field and taking into account interactions between itinerant and localized electrons [30,31,23,24,25,26]. These results show many novel phenomenon like charge and orbital ordering and metal-insulator transition as a function of electron correlations and filling of the electrons.…”