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Phase Transitions

Phase transitions in the Falicov–Kimball model away from half-filling

Martin Žonda

Published Oct 24, 2011• 7 citations
Publisher

Abstract

The canonical Monte Carlo method is used to study the order-disorder phase transition of the Falicov–Kimball model away from half-filling. It is shown that the transition from various inhomogeneous ground-state phases to the disordered phase can be either direct or indirect. The indirect transition means that the ground-state phase first, at critical temperature τ c , changes to a different ordered phase and at the temperature, that can be several times higher than τ c , finally changes to the disordered phase. It is shown that the Falicov–Kimball model, depending on the ground state phase, undergoes first order or second order phase transition or can even undergo both for the same parameters and different temperatures if the transition from the ground-state phase to the disordered phase is indirect.

DOI
10.1080/01411594.2011.604509

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The canonical Monte Carlo method is used to study the order-disorder phase transition of the Falicov–Kimball model away from half-filling. It is shown that the transition from various inhomogeneous ground-state phases to the disordered phase can be either direct or indirect. The indirect transition means that the ground-state phase first, at critical temperature τ c , changes to a different ordered phase and at the temperature, that can be several times higher than τ c , finally changes to the disordered phase. It is shown that the Falicov–Kimball model, depending on the ground state phase, undergoes first order or second order phase transition or can even undergo both for the same parameters and different temperatures if the transition from the ground-state phase to the disordered phase is indirect.
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.
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 one-dimensional spinless Falicov–Kimball (FKM) model is studied in the strong coupling limit away from half-filling. The small-cluster exact-diagonalization calculations are employed to obtain valence transitions in the ground state and for finite temperatures. It is found that in the ground state, the model describes continuous valence transitions for small band-fillings and both continuous and discontinuous transitions near half-filling. At finite temperatures, only continuous valence transitions are obtained. The valence is integer at low temperatures for small band-fillings and in other cases, it takes only intermediate values.
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.