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Register a new userGeneralized Falicov-Kimball Models
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In this paper we extend the Falicov-Kimball model (FKM) to the case where the quasi-particles entering the FKM are not ordinary fermions. As an example we first discuss how the FKM can be generalized to the case with spin-dependent hopping. Afterwards we discuss several cases where the quasi-particles entering the FKM are Majorana fermions (extended Majorana-Falicov-Kimball Model (MFKM). Two examples of extended MFKM are discussed in detail: (i) a $p$-wave BCS superconductor on a bipartite lattice and (ii) a BCS-Anderson model. We also discuss the most general forms of extended MFKM, including a brief discussion on the case where the Majorana fermions represent spins, but not real fermion particles.
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In this work, we study the extended Falicov-Kimball model at half-filling within the Hartree-Fock approach (HFA) (for various crystal lattices) and compare the results obtained with the rigorous ones derived within the dynamical mean field theory (DMFT). The model describes a system, where electrons with spin-$downarrow$ are itinerant (with hopping amplitude $t$), whereas those with spin-$uparrow$ are localized. The particles interact via on-site $U$ and intersite $V$ density-density Coulomb interactions. We show that the HFA description of the ground state properties of the model is equivalent to the exact DMFT solution and provides a qualitatively correct picture also for a range of small temperatures. It does capture the discontinuous transition between ordered phases at $U=2V$ for small temperatures as well as correct features of the continuous order-disorder transition. However, the HFA predicts that the discontinuous boundary ends at the isolated-critical point (of the liquid-gas type) and it does not merge with the continuous boundary. This approach cannot also describe properly a change of order of the continuous transition for large $V$ as well as various metal-insulator transitions found within the DMFT.
The observation of charge stripe order in the doped nickelate and cuprate materials has motivated much theoretical effort to understand the underlying mechanism of the stripe phase. Numerical studies of the Hubbard model show two possibilities: (i) stripe order arises from a tendency toward phase separation and its competition with the long-range Coulomb interaction or (ii) stripe order inherently arises as a compromise between itinerancy and magnetic interactions. Here we determine the restricted phase diagrams of the two-dimensional Falicov-Kimball model and see that it displays rich behavior illustrating both possibilities in different regions of the phase diagram.
Using exact numerical techniques we investigate the nature of excitonic (electron-hole) bound states and the development of exciton coherence in the one-dimensional half-filled extended Falicov-Kimball model. The ground-state phase diagram of the model exhibits, besides band insulator and staggered orbital ordered phases, an excitonic insulator (EI) with power-law correlations. The criticality of the EI state shows up in the von Neumann entropy. The anomalous spectral function and condensation amplitude provide the binding energy and coherence length of the electron-hole pairs which, on their part, point towards a Coulomb interaction driven crossover from BCS-like electron-hole pairing fluctuations to tightly bound excitons. We show that while a mass imbalance between electrons and holes does not affect the location of the BCS-BEC crossover regime it favors staggered orbital ordering to the disadvantage of the EI. Within the BEC regime the quasiparticle dispersion develops a flat valence-band top in accord with the experimental finding for Ta$_2$NiSe$_5$.
We derive an analytical expression for the local two-particle vertex of the Falicov-Kimball model, including its dependence on all three frequencies, the full vertex and all reducible vertices. This allows us to calculate the self energy in diagrammatic extensions of dynamical mean field theory, specifically in the dual fermion and the one-particle irreducible approach. Non-local correlations are thence included and originate here from charge density wave fluctuations. At low temperatures and in two dimensions, they lead to a larger self energy contribution at low frequencies and a more insulating spectrum.
A single transport relaxation rate governs the decay of both, longitudinal and Hall currents in Landau Fermi Liquids (LFL). Breakdown of this fundamental feature, first observed in cuprates and subsequently in other three-dimensional correlated systems close to (partial or complete) Mott metal-insulator transitions, played a pivotal role in emergence of a non-Landau Fermi liquid paradigm in higher dimensions $D(>1)$. Motivated hereby, we explore the emergence of this two relaxation rates scenario in the Hubbard-Falicov-Kimball model (HFKM) using the dynamical mean-field theory (DMFT). Specializing to $D=3$, we find, beyond a critical FK interaction, that two distinct relaxation rates governing distinct temperature ($T$) dependence of the longitudinal and Hall currents naturally emerges in the non-LFL metal. We rationalize this surprising finding by an analytical analysis of the structure of charge and spin correlations in the underlying impurity problem, and point out good accord with observations in the famed case of V$_{2-y}$O$_3$ near the MIT.
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