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Register a new userA complete devils staircase in the Falicov-Kimball model
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Added by
Cristian Micheletti
Publication date
1996
fields
Physics
and research's language is
English
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We consider the neutral, one-dimensional Falicov-Kimball model at zero temperature in the limit of a large electron--ion attractive potential, U. By calculating the general n-ion interaction terms to leading order in 1/U we argue that the ground-state of the model exhibits the behavior of a complete devils staircase.
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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.
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.
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$_5$.
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.
A numerical diagonalization technique with canonical Monte-Carlo simulation 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 ($t^{prime}$). It is observed that the low temperature ordered phases (i.e. regular, bounded and segregated) persist up to a finite critical temperature ($T_{c}$). In addition, we observe that the critical temperature decreases with increasing the correlated hopping in regular and bounded phases whereas it increases in the segregated phase. Single and multi peak patterns seen in the temperature dependence of specific heat ($C_v$) and charge susceptibility ($chi$) for different values of parameters like on-site Coulomb correlation strength ($U$), correlated hopping ($t^{prime}$) and filling of localized electrons ($n_{f}$) are also discussed.
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