Ground-state phase diagrams of the generalized Falicov-Kimball model with Hund coupling

Charge and spin orderings are studied on the simplest 1D and the 2D square lattice within the generalized Falicov-Kimball model with Hund coupling between localized and itinerant electrons. Using the restricted phase diagrams method (RPDM) a number of simple rules of formation of various sorts of ground state phases have been detected. In particular, relationships between density of current carriers (electrons or holes) and type of charge and magnetic arrangement has been determined. In 2D in the mixed valence regime only axial stripes (vertical or horizontal) have been found for intermediate values of the coupling constants. They are composed of ferromagnetic or antiferromagnetic chains interchanged with non-magnetic ones. For band fillings close to the half filling stripe phases oriented along one of the main diagonal direction are formed. The results suggest a possibility of tuning modulations of charge and magnetic superstructures with a change of doping.Comment: 10 pages, 6 figures; Fig. 2 slightly modified and the text adjusted accordingly, references adde

Extended Falicov-Kimball model: Hartree-Fock vs DMFT approach

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.Comment: 13 pages, 7 figures; pdfReVTex class. This is the Accepted Manuscript version (author created) of an article accepted for publication in J. Phys.: Condens. Matter. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The article has been published on a gold open access basis under a CC BY 3.0 licenc

Model of charge and magnetic order formation in itinerant electron systems

We propose a simple model of charge and/or magnetic order formation in systems containing both localized and itinerant electrons coupled by the on-site, spin-dependent interaction that represents Coulomb repulsion and Hund's rule (a generalized Falicov-Kimball model). Ground state properties of the model are analyzed on the square lattice on a basis of the phase diagrams that have been constructed rigorously, but in a restricted configurational space. For intermediate values of the coupling constants there are considerable ranges of itinerant electron densities where phases with complex charge and magnetic structures of the localized electrons have lower energy than the simplest antiferro- and ferromagnetic ones. A strong tendency towards the antiferromagnetic coupling between spins of localized electrons has been observed close to half-filling for any density of localized electrons, including situations where the magnetic ions are diluted. For small band fillings the ferromagnetic coupling between localized spins is predominant.Comment: 13 pages, 5 figure

Gapless metallic charge-density-wave phase driven by strong electron correlations

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 $\Delta$ at the Fermi level $\varepsilon_F=0$, which is proportional to the interaction constant $U$. With an increase of $T$ the $DOS$ evolves in various ways that depend on $U$. For $U>U_{cr}$ the gap persists for any $T$ (then $\Delta >0$), so the system is always an insulator. However, if $U < U_{cr}$, two additional subbands develop inside the gap. They become wider with increasing $T$ and at a certain $U$-dependent temperature $T_{MI}$ they join with each other at $\varepsilon_F$. Since above $T_{MI}$ the $DOS$ is positive at $\varepsilon_F$, we interpret $T_{MI}$ as the transformation temperature from insulator to metal. It appears, that $T_{MI}$ approaches the order-disorder phase transition temperature $T_{O-DO}$ when $U$ is close to 0 or $U_{cr}$, but $T_{MI}$ is substantially lower than $T_{O-DO}$ for intermediate values of $U$. 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 $\Delta$ 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.Comment: 19 pages, 9 figures; submitted to Physical Review