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Physical review. B, Condensed matter

Thermodynamics of the Falicov-Kimball model with two spinless impurities interacting with a fermionic bath

Luis R. Ramos, W. C. Oliveira, Valter L. Líbero

Published Feb 10, 2003• 4 citations
Publisher

Abstract

Specific heat and charge susceptibility are computed for the Falicov-Kimball model with two spinless impurities embedded in a fermionic bath. The model takes into account the Coulomb scattering and hybridization between local levels and conduction states. The numerical renormalization group with two discretization parameters is used to obtain the spectrum of the model, from which the thermodynamic is obtained. We discuss the importance of going beyond the usual approximation that projects all momenta at the Fermi level.

DOI
10.1103/physrevb.67.085104

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Specific heat and charge susceptibility are computed for the Falicov-Kimball model with two spinless impurities embedded in a fermionic bath. The model takes into account the Coulomb scattering and hybridization between local levels and conduction states. The numerical renormalization group with two discretization parameters is used to obtain the spectrum of the model, from which the thermodynamic is obtained. We discuss the importance of going beyond the usual approximation that projects all momenta at the Fermi level.
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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 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 spinless Falicov-Kimball model is studied by the use of a recently developed projector-based renormalization method for many-particle Hamiltonians. The method is used to evaluate static and dynamic quantities of the one-dimensional model at half-filling. These include the quasiparticle excitation energy ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}}_{k}$, the momentum distribution nk{n}_{k}nk​ of the conduction electrons, and the spatial correlation functions of the localized electrons. One of the most remarkable results is the appearance of a gap in ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}}_{k}$ at the Fermi level of the order of the Coulomb repulsion UUU, which is accompanied by a smooth behavior for nk{n}_{k}nk​. The density of states for the conduction electrons and the one-particle spectral functions for the localized electrons are also discussed. In both quantities, a gap opens with increasing UUU.
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 density matrix renormalization group method is used to examine possibilities of electronic ferroelectricity in the spinless Falicov-Kimball model. The model is studied for a wide range of parameters including weak and strong interactions as well as the symmetric and unsymmetric case. In all examined cases the 〈d+f〉〈{d}^{+}f〉〈d+f〉-expectation value vanishes for vanishing hybridization V, indicating that the spinless Falicov-Kimball model does not allow for a ferroelectric ground state with a spontaneous polarization.