A ground state phase diagram of a spinless, extended Falicov–Kimball model on the triangular lattice

Abstract

Correlated systems with hexagonal layered structures have come to fore with renewed interest in Cobaltates, transition-metal dichalcogenides and GdI2. While superconductivity, unusual metal and possible exotic states (prevented from long range order by strong local fluctuations) appear to come from frustration and correlation working in tandem in such systems, they freeze at lower temperature to crystalline states. The underlying effective Hamiltonian in some of these systems is believed to be the Falicov-Kimball model and therefore, a thorough study of the ground state of this model and its extended version on a non-bipartite lattice is important. Using a Monte Carlo search algorithm, we identify a large number of different possible ground states with charge order as well as valence and metal-insulator transitions. Such competing states, close in energy, give rise to the complex charge order and other broken symmetry structures as well as phase segregations observed in the ground state of these systems.

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

“…(x) After this classical Monte Carlo simulation algorithm is used to achieve an unique ground state configuration by annealing the static classical variables {ω σ } ramping the temperature down from a high value to a very low value [23].…”

“…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.…”

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].…”

Classical and Quantum Liquids Induced by Quantum Fluctuations

“…The melting of the CDW state with increasing T was observed for commensurate fillings [15][16][17][18]. On the triangular lattice the FKM and its extensions display a variety of different ground-state phases [19][20][21][22][23]. For incommensurate fillings the FKM favors phase separation [5].…”