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Acta Physica Polonica A

Thermodynamics of the Generalized Spin-One-Half Falicov-Kimball Model in Two Dimensions

Martin Žonda, Pavol Farkašovský, Hana Čenčariková

Published Jan 1, 2009• 0 citations
Publisher

Abstract

The extrapolation of small-cluster exact-diagonalization calculations and the Monte Carlo method is used to study the spin-one-half Falicov-Kimball model extended by the spin-dependent Coulomb interaction (J) between the localized f and itinerant d electrons as well as the on-site Coulomb interaction (U f f ) between the localized f electrons.It is shown that in the symmetric case the ground-state phase diagram of the model has an extremely simple structure that consists of only two phases, and namely, the charge-density-wave phase and the spin-density-wave phase.The nonzero temperature studies showed that these phases persist also at finite temperatures.The same calculations that we performed for unsymmetric case showed that charge and spin ordering can be destroyed simultaneously or consecutively.

DOI
10.12693/aphyspola.115.104

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The extrapolation of small-cluster exact-diagonalization calculations and the Monte Carlo method is used to study the spin-one-half Falicov-Kimball model extended by the spin-dependent Coulomb interaction (J) between the localized f and itinerant d electrons as well as the on-site Coulomb interaction (U f f ) between the localized f electrons.It is shown that in the symmetric case the ground-state phase diagram of the model has an extremely simple structure that consists of only two phases, and namely, the charge-density-wave phase and the spin-density-wave phase.The nonzero temperature studies showed that these phases persist also at finite temperatures.The same calculations that we performed for unsymmetric case showed that charge and spin ordering can be destroyed simultaneously or consecutively.
The two-dimensional Falicov-Kimball (FK) model is analyzed using the Monte Carlo method. In the case of concentrations of both itinerant and localized particles equal to 0.5 we determine temperature dependence of specific heat, charge density wave susceptibility, and density-density correlation function. In the weak interaction regime we find a first order transition to the ordered state and anomalous temperature dependence of the correlation function. We construct the phase diagram of half-filled FK model. Also, the role of next-nearest-neighbor hopping on the phase diagram is analyzed. Lastly, we discuss the density of states and the spectral functions for the mobile particles in weak and strong interaction regime.
The extended Falicov-Kimball model is analyzed exactly in the ground state at half filling in the limit of large dimensions. In the model the on-site and the intersite density-density interactions between all particles are included. We determined the model's phase diagram and found a discontinuous transition between two different charge-ordered phases. Our analytical calculations show that the ground state of the system is insulating for any nonzero values of the interaction couplings. We also show that the dynamical mean-field theory and the static broken-symmetry Hartree-Fock mean-field approximation give the same results for the model at zero temperature. In addition, we prove using analytical expressions that at infinitesimally small, but finite, temperatures the system can be metallic.
The two-dimensional Falicov-Kimball (FK) model is analyzed using Monte Carlo method. In the case of concentrations of both itinerant and localized particles equal to 0.5 we determine temperature dependence of specific heat, charge density wave susceptibility and density-density correlation function. In the weak interaction regime we find a first order transition to the ordered state and anomalous temperature dependence of the correlation function. We construct the phase diagram of half-filled FK model. Also, the role of next-nearest-neighbor hopping on the phase diagram is analyzed. Lastly, we discuss the density of states and the spectral functions for the mobile particles in weak and strong interaction regime.
Charge and spin orderings are studied on the simplest one-dimensional (1D) and the two-dimensional (2D) square lattices within the generalized Falicov-Kimball model with Hund coupling between localized and itinerant electrons. Using the restricted phase diagram method (RPDM), a number of simple rules of formation of various sorts of ground-state phases have been detected. In particular, relationships between density of current carriers (electrons or holes) and type of charge and magnetic arrangement have been determined. In two dimensions in the mixed-valence regime, only axial stripes (vertical or horizontal) have been found for intermediate values of the coupling constants. They are composed of ferromagnetic or antiferromagnetic chains interchanged with nonmagnetic ones. For band fillings close to the half filling, stripe phases oriented along one of the main diagonal direction are formed. The results suggest the possibility of tuning modulations of charge and magnetic superstructures with a change in doping.
The Falicov-Kimball model supplemented with the Ising-type Hund coupling describes charge and magnetic order induced by on-site, charge-, and spin-dependent interactions between itinerant electrons and localized ions. Motivated by a discovery of the rich structure of ground-state phase diagrams containing various charge and magnetic superstructures, we analyze the energy spectrum and determine numerically finite temperature properties of the model on the square $4\ifmmode\times\else\texttimes\fi{}4$ cluster at half filling. For the density of magnetic ions equal to 1 and 1/2 and not too small coupling constants we show that many-electron collective excitations derived from changes in positions of the ions or inversions their spins have much lower energy than single-electron excitations. From an analysis of the excitation spectrum structure we derive effective interactions between the ions. When the coupling constants are large enough the interactions reduce to two-body forces between ions occupying the nearest-neighboring sites. Finite-temperature characteristics and temperatures of transformation from charge or magnetically ordered to disordered phases are determined in the wide range of the interaction couplings.
The finite-temperature properties of the three-dimensional Falicov-Kimball model are studied in the symmetric case using the classical Monte-Carlo method. Analysing the temperature dependence of the specific heat C V,N we have found that the system exhibits the phase transition from the low-temperature ordered phase to the high-temperature disordered phase. The critical temperature of the phase transition is calculated numerically from the position of the maximum of C V,N and it is shown that its value in the three-dimensional case is considerably enhanced in comparison to the two-dimensional case. In addition, the temperature dependence of the itinerant electron density of states (DOS) is analysed. For very low-temperatures we have observed a formation of fine structure inside the principal gap that transforms to a pseudo-gap at higher temperatures and becomes temperature independent for sufficiently large temperatures. In this temperature region we have calculated DOS for different Coulomb interactions and found the Mott-Hubbard metal-insulator transition.