The ground-state density of states of the half-filled Falicov-Kimball model contains a charge-density-wave gap. At finite temperature, this gap is not immediately closed, but is rather filled in by subgap states. For a specific combination of parameters, this leads to a stable phase where the system is in an ordered charge-density-wave phase, but there is high density of states at the Fermi level. We show that this property can be, in finite dimensions, traced to a crossing of sharp states resulting from the single particle excitations of the localized subsystem. The analysis of the inverse participation ratio points to a strong localization in the discussed regime. However, the pronounced subgap density of states can still lead to a notable increase of charge transport through a finite size system. We show this by focusing on the transmission in heterostructures where a Falicov-Kimball system is sandwiched between two metallic leads.
The ground-state density of states of the half-filled Falicov-Kimball model contains a charge-density-wave gap. At finite temperature, this gap is not immediately closed, but is rather filled in by subgap states. For a specific combination of parameters, this leads to a stable phase where the system is in an ordered charge-density-wave phase, but there is high density of states at the Fermi level. We show that this property can be, in finite dimensions, traced to a crossing of sharp states resulting from the single particle excitations of the localized subsystem. The analysis of the inverse participation ratio points to a strong localization in the discussed regime. However, the pronounced subgap density of states can still lead to a notable increase of charge transport through a finite size system. We show this by focusing on the transmission in heterostructures where a Falicov-Kimball system is sandwiched between two metallic leads.
We analyze the transformation from insulator to metal induced by thermal fluctuations within the Falicov-Kimball model. Using the dynamic mean field theory (DMFT) formalism on the Bethe lattice we find rigorously the temperature dependent density of states (DOS) at half filling in the limit of high dimensions. At zero temperature (T=0) the system is ordered to form the checkerboard pattern and the DOS has the gap $\ensuremath{\Delta}$ at the Fermi level ${\ensuremath{\varepsilon}}_{F}=0$, which is proportional to the interaction constant U. With an increase of T the DOS evolves in various ways that depend on U. For U>Ucr the gap persists for any T (then $\ensuremath{\Delta}>0$), so the system is always an insulator. However, if U<Ucr, two additional subbands develop inside the gap. They become wider with increasing T and at a certain U-dependent temperature TMI they join with each other at ${\ensuremath{\varepsilon}}_{F}$. Since above TMI the DOS is positive at ${\ensuremath{\varepsilon}}_{F}$, we interpret TMI as the transformation temperature from insulator to metal. It appears that TMI approaches the order-disorder phase transition temperature ${T}_{\mathrm{O}\text{\ensuremath{-}}\mathrm{DO}}$ when U is close to 0 or Ucr, but TMI is substantially lower than ${T}_{\mathrm{O}\text{\ensuremath{-}}\mathrm{DO}}$ for intermediate values of U. Moreover, using an analytical formula we show that TMI=0 at U=2<Ucr, so we prove that the quantum critical point exists for the ordered metal at (T=0,U=2). Having calculated the temperature dependent DOS we study thermodynamic properties of the system starting from its free energy F. Then we find how the order parameter d and the gap $\ensuremath{\Delta}$ change with T and we construct the phase diagram in the variables T and U, where we display regions of stability of four different phases: ordered insulator, ordered metal, disordered insulator, and disordered metal. Finally, we use a low temperature expansion to demonstrate the existence of a nonzero DOS at a characteristic value of U on a general bipartite lattice.
Employing a combination of a sign-problem-free Monte Carlo approach and nonequilibrium Green's-function techniques, we study nonequilibrium charge transport in a model heterostructure, where a two-dimensional spinless Falicov-Kimball system is coupled to two noninteracting leads. We show that the transport characteristic depends sensitively on the electrostatic potential in the system and exhibits different properties for different phases of the Falicov-Kimball model. In particular, pronounced steplike changes of the current and transmission are observed at the phase boundaries, evident even on a logarithmic scale. Analyzing finite-size effects, we find that with the method used a relatively small system can be utilized to address specific thermodynamic limits. Phenomenon of the localization is discussed as well.
We study the spectral properties of the charge-density-wave (CDW) phase of the half-filled spinless Falicov-Kimball model within the framework of the dynamical mean field theory. We present detailed results for the spectral function in the CDW phase as a function of temperature and U. We show how the proximity of the non-Fermi liquid phase affects the CDW phase, and show that there is a region in the phase diagram where we get a CDW phase without a gap in the spectral function. This is a radical deviation from the mean-field prediction where the gap is proportional to the order parameter.
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 spinless Falicov-Kimball model is solved exactly in the limit of infinite dimensions on both the hypercubic and Bethe lattices. The competition between segregation, which is present for large U, and charge-density-wave order, which is prevalent at moderate U, is examined in detail. We find a rich phase diagram that displays both of these phases. The model also shows nonanalytic behavior in the charge-density-wave transition temperature when U is large enough to generate a correlation-induced gap in the single-particle density of states.
Abstract We present a systematic investigation of the stability of the phase diagram of the spinless Falicov–Kimball model on two-dimensional non-bipartite lattices, the triangular and kagome lattices, using Markov-chain Monte Carlo simulations. Three filling or chemical potential conditions are examined: fixed chemical potentials ( μf=μc=U/2 μ f = μ c = U / 2 ), “generalized” half-filling ( nˉf=1/3 n ¯ f = 1 / 3 , nˉc=2/3 n ¯ c = 2 / 3 ), and conventional half-filling ( nˉf=nˉc=1/2 n ¯ f = n ¯ c = 1 / 2 ). For each condition, the effects of a perturbatively small next-nearest-neighbor hopping are studied. On the triangular lattice, Anderson insulator, Mott insulator, and charge-density wave (CDW) phases are found in all cases, with the CDW driven by Coulomb interaction-mediated nesting. Evidence for a charge-liquid regime is found in the region between the weakly correlated regime and the CDW, characterized by competing charge-ordering wavevectors and the absence of universal scaling behavior, whose extent shrinks progressively from the grand-canonical to the conventional half-filling condition. On the kagome lattice, the CDW phase is completely absent; instead, an insulating ground state, plausibly of the Mott type, is found, with signatures of a possible quantum phase transition at zero temperature. Our results establish the crucial role of lattice geometry and particle-hole symmetry breaking in shaping the phase diagram of correlated electron systems. Graphical abstract The 2d triangular lattice (left) and the 2d kagome lattice (right) with their unit cells highlighted. Bottom: The corresponding phase diagram of the Falicov-Kimball model (FKM) on each lattice, illustrating the non-Fermi liquid (nFL), charge-density wave (CDW), Anderson insulator (AI) and Mott insulator (MI) regimes.