Thermodynamics of the two-dimensional Falicov-Kimball model: A classical Monte Carlo study

Abstract

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.

Energy spectrum analysis and finite temperature properties of the Falicov-Kimball model with Hund coupling at half filling

“…However, we notice that for not too small values of the parameters U or J, some our results are consistent with a few available data obtained, either exactly in the thermodynamic limit ͑as for example energies per site of the antiferromagnetic and ferromagnetic phase 18 ͒ or by the Monte Carlo method for larger systems. 15 Indeed, the results we obtained for the charge order in the case of J = 0 are very similar to the results reported for the spinless FKM. 15 However, since in our case the number of itinerant electrons is doubled ͑as compare to the spinless case͒ the effective forces between localized particles and transformation temperatures are two times higher than in the spinless system.…”

“…15 Indeed, the results we obtained for the charge order in the case of J = 0 are very similar to the results reported for the spinless FKM. 15 However, since in our case the number of itinerant electrons is doubled ͑as compare to the spinless case͒ the effective forces between localized particles and transformation temperatures are two times higher than in the spinless system.…”

“…Actually, the same assumption was made in the Monte Carlo studies. 15 Then the system can be excited either by pushing up electrons from levels lying below the Fermi energy to above it ͑single electron excitations͒ or by changing positions and/or spin orientations of the magnetic ions. In the latter case, the sequence of single electron energy levels is modified and the excitation energy is equal to the difference between the Fermi sea energy of the modified sequence and the sequence assigned to the ground-state configuration.…”

Momentum distribution and ordering in mixtures of ultracold light- and heavy-fermion atoms

“…The model is solved by means of a variation of the Monte Carlo (MC) method. The method is based on the classical METROPOLIS algorithm modified in such a way that systems with both quantum and classical degrees of freedom can be simulated [16]. In each MC step, a new configuration of the heavy atoms is generated.…”

Fermions and Bosons in a Double-Well Potential

“…Such a conguration in a bulk system would correspond to a superposition of two equivalent chessboard states, where fermions occupy one sublattice and bosons the other one [22,23].…”