Two-dimensional Falicov-Kimball Model Research Articles

Orthogonal metal in the Hubbard model with liberated slave spins

A two-dimensional Falicov-Kimball model, equivalent to the Hubbard model in an unconstrained slave-spin representation, is studied by quantum Monte Carlo simulations. The focus is on a fractionalized metallic phase that is characterized in terms of spectral, thermodynamic, and transport properties, including a comparison to the half-filled Hubbard model. The properties of this phase, most notably a single-particle gap but gapless spin and charge excitations, can in principle be understood in the framework of orthogonal metals. However, important and interesting differences arise in the present setting compared to single-particle mean-field theories and other models. We also discuss the role of the local constraints from the slave-spin representation within an extended phase diagram that includes the spatial dimension as a parameter, thereby making contact with previous work in infinite dimensions. Finally, we highlight the absence of $\pi$-flux configurations in the slave-spin formulation, in particular in the context of topologically ordered fractional phases predicted at the mean-field level.

Spreading of correlations in the Falicov-Kimball model

We study dynamical properties of the one- and two-dimensional Falicov-Kimball model using lattice Monte Carlo simulations. In particular, we calculate the spreading of charge correlations in the equilibrium model and after an interaction quench. The results show a reduction of the light-cone velocity with interaction strength at low temperature, while the phase velocity increases. At higher temperature, the initial spreading is determined by the Fermi velocity of the noninteracting system and the maximum range of the correlations decreases with increasing interaction strength. Charge order correlations in the disorder potential enhance the range of the correlations. We also use the numerically exact lattice Monte Carlo results to benchmark the accuracy of equilibrium and nonequilibrium dynamical cluster approximation calculations. It is shown that the bias introduced by the mapping to a periodized cluster is substantial, and that from a numerical point of view, it is more efficient to simulate the lattice model directly.

Nonequilibrium dynamical cluster approximation study of the Falicov-Kimball model

We use a nonequilibrium implementation of the dynamical cluster approximation (DCA) to study the effect of short-range correlations on the dynamics of the two-dimensional Falicov-Kimball model after an interaction quench. As in the case of single-site dynamical mean field theory, thermalization is absent in DCA simulations, and for quenches across the metal-insulator boundary, nearest-neighbor charge correlations in the nonthermal steady state are found to be larger than in the thermal state with identical energy. We investigate to what extent it is possible to define an effective temperature of the trapped state after a quench. Based on the ratio between the lesser and retarded Green's function we conclude that a roughly thermal distribution is reached within the energy intervals corresponding to the momentum-patch dependent subbands of the spectral function. The effectively different chemical potentials of these distributions however lead to a very hot, or even negative, effective temperature in the energy intervals between these subbands.

Interaction-Tuned Anderson versus Mott Localization.

Disorder or sufficiently strong interactions can render a metallic state unstable, causing it to turn into an insulating one. Despite the fact that the interplay of these two routes to a vanishing conductivity has been a central research topic, a unifying picture has not emerged so far. Here, we establish that the two-dimensional Falicov-Kimball model, one of the simplest lattice models of strong electron correlation, does allow for the study of this interplay. In particular, we show that this model at particle-hole symmetry possesses three distinct thermodynamic insulating phases and exhibits Anderson localization. The previously reported metallic phase is identified as a finite-size feature due to the presence of weak localization. We characterize these phases by their electronic density of states, staggered occupation, conductivity, and the generalized inverse participation ratio. The implications of our findings for other strongly correlated systems are discussed.

The possibility of detection of finite temperature stripe ordering in 2D spinless Falicov–Kimball model

This paper announces a possibility of detection of finite-temperature stripe ordering in the two-dimensional Falicov–Kimball model at half-filling by extensive Monte Carlo simulations. Moreover, the tools to study orderings and to detect phase transition temperatures are presented. The use of Binder's cumulant is supplemented by finite-size magnetization profiles not analyzed previously in this context. Continuous character of phase transitions is announced. Analyses proving the existence of more complicated phases of finite-temperature stripe ordering than the checkerboard one conclude the paper.

Phase transitions in the spinless Falicov-Kimball model with correlated hopping

The canonical Monte-Carlo is used to study the phase transitions from the low-temperature ordered phase to the high-temperature disordered phase in the two-dimensional Falicov-Kimball model with correlated hopping. As the low-temperature ordered phase we consider the chessboard phase, the axial striped phase and the segregated phase. It is shown that all three phases persist also at finite temperatures (up to the critical temperature $\tau_c$) and that the phase transition at the critical point is of the first order for the chessboard and axial striped phase and of the second order for the segregated phase. In addition, it is found that the critical temperature is reduced with the increasing amplitude of correlated hopping $t'$ in the chessboard phase and it is strongly enhanced by $t'$ in the axial striped and segregated phase.

Electronic structure of the Falicov-Kimball model with a magnetic field: Dynamical mean-field study

The two-dimensional Falicov-Kimball model in the presence of a perpendicular magnetic field is investigated by the dynamical mean-field theory. Within the model the interplay between electron correlations and the fine electron structure due to the magnetic field is essentially emerged. Without electron correlations the magnetic field induces the electron structure to the so-called Hofstadter butterfly. It is found that when electron correlations drives the metal-insulator transition, they simultaneously smear out the fine structure of the Hofstadter butterfly. In a long-range ordered phase, the electron correlation induced gap preserves the fine structure, but it separates the Hofstadter butterfly into two wings.

Statistics of local density of states in the Falicov-Kimball model with local disorder

Statistics of the local density of states in the two-dimensional Falicov-Kimball model with local disorder is studied by employing the statistical dynamical mean-field theory. Within the theory, the local density of states and its distributions are calculated through stochastic self-consistent equations. The most probable value of the local density of states is used to monitor the metal-insulator transition driven by correlation and disorder. Nonvanishing of the most probable value of the local density of states at the Fermi energy indicates the existence of extended states in the two-dimensional disordered interacting system. It is also found that the most probable value of the local density of states exhibits a discontinuity when the system crosses from extended states to the Anderson localization. A phase diagram is also presented.

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

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.

Phase Diagram of the Two-dimensional t–t′ Falicov-Kimball Model

The ground-state phase diagram of the two-dimensional Falicov-Kimball model with nearest-neighbour and next-nearest-neighbour hoppings has been studied in the perturbative regime where hoppings are small compared with the on-site Coulomb interaction. The phase diagram at fourth-order exhibits a richer structure than the one of the ordinary Falicov-Kimball model.

Ground states of the two-dimensional Falicov–Kimball model with correlated hopping

A recently developed numerical method, based on the exact-diagonalization calculations, is used to study ground states of the two-dimensional Falicov–Kimball model (FKM) with correlated hopping ( t ′ ) in the symmetric case. It is shown that the ground-state phase diagram as well as the picture of valence and metal–insulator transitions found for the conventional FKM (without correlated hopping) are strongly changed when the correlated hopping term is added. In particular, it was found that for intermediate t ′ and f level energy E f < 0 , the phases with noninteger valency are suppressed and the metallic phase disappears. On the other hand, for strong t ′ , the metallic phase is stabilized for a wide region of model parameters.

Stripe phases in the two-dimensional Falicov-Kimball model.

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 diagram of the two-dimensional Falicov-Kimball model and see that it displays rich behavior illustrating both possibilities in different regions.

Correlated hopping in the Falicov-Kimball model: a dynamical mean-field study

We study the effects of correlated hopping in the two-dimensional (2D) Falicov-Kimball model by means ofan extension of the dynamical mean-field approximation (DMFA).The extension is based on the projection technique and the DMFA,in which nonlocal correlations are taken into account through static quantitiesof a relevant subspace.The effect of the correlated hopping is to introduce nonlocal self-energy componentswhich remain even at D→∞. We show thatthe sum rules of the spectral function and its moments are preserved.The spectral function obtained reveals significant nonlocal contributions which are absent in the DMFA.

Dynamical cluster approximation: Nonlocal dynamics of correlated electron systems

We recently introduced the dynamical cluster approximation(DCA), a new technique that includes short-ranged dynamical correlations in addition to the local dynamics of the dynamical mean field approximation while preserving causality. The technique is based on an iterative self-consistency scheme on a finite size periodic cluster. The dynamical mean field approximation (exact result) is obtained by taking the cluster to a single site (the thermodynamic limit). Here, we provide details of our method, explicitly show that it is causal, systematic, $\Phi$-derivable, and that it becomes conserving as the cluster size increases. We demonstrate the DCA by applying it to a Quantum Monte Carlo and Exact Enumeration study of the two-dimensional Falicov-Kimball model. The resulting spectral functions preserve causality, and the spectra and the CDW transition temperature converge quickly and systematically to the thermodynamic limit as the cluster size increases.

Ground State Properties¶of the Neutral Falicov-Kimball Model

We determine the large U ground states in the neutral two-dimensional Falicov–Kimball model for a sequence of densities converging to 0. For rational densities in (1/6,2/11) we show that the ground states exhibit a phase separation.

Non-local effects in the fermion dynamical mean-field framework; application to the two-dimensional Falicov-Kimball model

We propose a new, controlled approximation scheme that explicitly includes the effects of non-local correlations on the D = solution. In contrast to the usual D = case, the self-energy is self-consistently coupled to two-particle correlation functions. The formalism is general, and is applied to the two-dimensional Falicov-Kimball model. Our approach possesses all the strengths of the large-D solution, and allows one to undertake a systematic study of the effects of inclusion of k-dependent effects on the D = picture. Results for the density of states (), and the single-particle spectral density for the 2D Falicov-Kimball model always yield positive definite (), and the spectral function shows striking new features inaccessible for D = . Our results are in good agreement with the exact results known from the 2D Falicov-Kimball model.

Ground states and flux configurations of the two-dimensional Falicov-Kimball model

The Falicov-Kimball model is a lattice model of itinerant spinless fermions (electrons) interacting by an on-site potential with classical particles (ions). We continue the investigations of the crystalline ground states that appear for various filling of electrons and ions for large coupling. We investigate the model for square as well as triangular lattices. New ground states are found and the effects of a magnetic flux on the structure of the phase diagram are studied. The flux phase problem where one has to find the optimal flux configurations and the nuclei configurations is also solved in some cases. Finally we consider a model where the fermions are replaced by hard-core bosons. This model also has crystalline ground states. Therefore their existence does not require the Pauli principle, but only the on-site hard-core constraint for the itinerant particles.

The two-dimensional Falicov-Kimball model at finite temperatures: numerical studies

The finite temperature properties of the spinless Falicov-Kimball model are studied in two dimensions using small-cluster exact-diagonalization calculations. The resultant exact solutions are used to examine the f-state occupation (nf), the specific heat (C) and the density of doubly occupied sites (d) as functions of temperature (τ), f-level energy (Ef) and the interaction strength U. A number of remarkable results are found. (i) In all cases nf and d are smooth functions of τ and Ef. No discontinuous transitions occur at finite temperatures. (ii) The specific-heat curves exhibit a broad single-peak structure of Shottky form (‖Ef‖ large), as well as a two-peak structure consisting of a sharp peak of Ising type followed by a broad peak of Shottky type (‖Ef‖ small). (iii) The specific-heat coefficient is extremely enhanced at low temperatures for some values of Ef. (iv) Depending on a range of parameters used, the system exhibits intermediate-valence behavior as well as some features of heavy-fermion behavior. The results are independent of the size of clusters for a wide range of parameters and can be used to interpret much of the experimental data of rare-earth compounds. Finally, the f-electron density-density correlation functions are calculated and the U-dependence of the critical temperature is discussed.

The ground-state phase diagram of the two-dimensional Falicov-Kimball model

The spinless Falicov-Kimball model on a two-dimensional square lattice is studied using the method of restricted phase diagrams constructed in the grand canonical ensemble. The results are compared with the one-dimensional model. Although the two-dimensional phase diagrams are more complex, with several distinct families of ion configurations occurring as ground states, there are surprising similarities with the one-dimensional case. Within each family of configurations, the ground states form a devil`s staircase structure and the configurations are constructed according to a composition rule identical to that in one dimension. It is also found that, as in one dimension, segregation occurs in the non-neutral model for large ion-electron interaction strength. Some features of the phase diagrams are understood by examining the effective two-body ion interaction.