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AIP conference proceedings

Thermodynamic studies of spin-1/2 Falicov-Kimball model (FKM) on a triangular lattice

Sant Kumar, Umesh K. Yadav, Tulika Maitra, Ishwar S Singh

Published Jan 1, 2016• 3 citations
Publisher

Abstract

Thermodynamic properties of the spin-dependent Falicov-Kimball model are studied on a triangular lattice for one-fourth filled case. Numerical diagonalization and Monte-Carlo simulation are used to study the thermodynamic properties. Continuous phase transitions are observed at finite temperature. We have observed that critical temperature (Tc) increases with the increase in on-site Coulomb correlation IJ. The second order nature of die transition is also revealed from the temperature dependence of specific heat.

DOI
10.1063/1.4947619

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Thermodynamic properties of the spin-dependent Falicov-Kimball model are studied on a triangular lattice for one-fourth filled case. Numerical diagonalization and Monte-Carlo simulation are used to study the thermodynamic properties. Continuous phase transitions are observed at finite temperature. We have observed that critical temperature (Tc) increases with the increase in on-site Coulomb correlation IJ. The second order nature of die transition is also revealed from the temperature dependence of specific heat.
The exact numerical diagonalization technique with canonical Monte-Carlo algorithm is used to study the phase transitions from low temperature (ordered) phase to high temperature (disordered) phase of spinless Falicov-Kimball model on a triangular lattice with correlated hopping (t'). The low temperature (regular, striped, bounded and segregated) phases persist up to a finite critical temperature (Tc). With increasing the correlated hopping the critical temperature decreases in regular, striped and bounded phases and exotically increases in segregated phase.
Combined effects of correlated electron hopping, electron correlations and orbital magnetic field are studied on ground state properties of spinless Falicov-Kimball model (FKM). Results are obtained for finite size triangular lattice with periodic boundary conditions using numerical diagonalization and Monte-Carlo simulation techniques. It is found that the ground state configurations of electrons strongly depend on correlated electron hopping, onsite Coulomb interaction and orbital magnetic field. Several interesting configurations e.g. regular, segregated, axial and diagonal striped and hexagonal phases are found with change in correlated hopping and magnetic field. Study of density of states reveals that magnetic field induces a metal to insulator transition accompanied by segregated phase to an ordered phase. These results are applicable to the systems of recent interest like GdI2, NaTiO2 and MgV2O4 and can also be seen experimentally in cold atomic set up.
The thermodynamic properties of the extended Falicov-Kimball model (FKM) for spinless fermions are studied as a function of temperature, doping, and interlevel spacing on the two-dimensional lattice. Thermodynamic quantities are calculated using the finite-temperature Lanczos method with additional phase averaging for a system of $4\ifmmode\times\else\texttimes\fi{}4$ sites. Changes of the thermodynamic properties are studied as the system evolves from its symmetric limit represented by the original Hubbard model to the other limiting case, which corresponds to the original FKM for spinless fermions. Our results indicate that valence transition exists in the extended Falicov-Kimball model.
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.
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.
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.