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Acta Physica Polonica A

One-Electron Excitations vs. Collective Excitations in the 1D Falicov-Kimball Model with Hund Coupling at Half Filling

Jakub Wrzodak, R. Lemański

Published Aug 1, 2010• 2 citations
Publisher

Abstract

The Falicov-Kimball model enriched with Ising-type Hund coupling between spins of itinerant electrons and magnetic ions is studied exactly on finite 1D rings.At half filling (one electron per site) and for the density of magnetic ions equal to 1/2 it is shown that many-electron collective excitations coupled to spin reorientations of the magnetic ions have much lower energy than single electron excitations.This property is caused by energy gaps formed at the Fermi levels in one-electron energy spectra of all relevant magnetic configurations of the ions.Consequently, low temperature properties of the system are not driven by one-particle, elementary electron excitations but many-particle collective excitations, where both electrons and spins of magnetic ions are involved.In addition, it is shown that many-body excitation spectra derived both from spin fluctuations and from charge fluctuations have a regular structure.

DOI
10.12693/aphyspola.118.366

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The Falicov-Kimball model enriched with Ising-type Hund coupling between spins of itinerant electrons and magnetic ions is studied exactly on finite 1D rings.At half filling (one electron per site) and for the density of magnetic ions equal to 1/2 it is shown that many-electron collective excitations coupled to spin reorientations of the magnetic ions have much lower energy than single electron excitations.This property is caused by energy gaps formed at the Fermi levels in one-electron energy spectra of all relevant magnetic configurations of the ions.Consequently, low temperature properties of the system are not driven by one-particle, elementary electron excitations but many-particle collective excitations, where both electrons and spins of magnetic ions are involved.In addition, it is shown that many-body excitation spectra derived both from spin fluctuations and from charge fluctuations have a regular structure.
The Falicov-Kimball model supplemented with the Ising-type Hund coupling describes charge and magnetic order induced by on-site, charge-, and spin-dependent interactions between itinerant electrons and localized ions. Motivated by a discovery of the rich structure of ground-state phase diagrams containing various charge and magnetic superstructures, we analyze the energy spectrum and determine numerically finite temperature properties of the model on the square $4\ifmmode\times\else\texttimes\fi{}4$ cluster at half filling. For the density of magnetic ions equal to 1 and 1/2 and not too small coupling constants we show that many-electron collective excitations derived from changes in positions of the ions or inversions their spins have much lower energy than single-electron excitations. From an analysis of the excitation spectrum structure we derive effective interactions between the ions. When the coupling constants are large enough the interactions reduce to two-body forces between ions occupying the nearest-neighboring sites. Finite-temperature characteristics and temperatures of transformation from charge or magnetically ordered to disordered phases are determined in the wide range of the interaction couplings.
In order to contribute to understand well the finite-temperature properties of the Falicov-Kimball model, we study the temperature dependence of the specific heat, internal energy, entropy, and mean square fluctuation of the difference between the ion and electron numbers, and of the correlation functions of the one-dimensional half-filled-band Falicov-Kimball model. For this purpose we used the method of small-cluster exact-diagonalization calculations with the application of the grand canonical ensemble and of extrapolation techniques to the infinite chain. Our results show that the examined Falicov-Kimball model exhibits behavior of alternate electron-ion short-range ordering at low temperature, and gradual metal-insulator transition at high temperature, but, does not exhibit the crossing point of the specific heat curves, characteristic of the Hubbard model.
The spinless Falicov-Kimball model is studied by the use of a recently developed projector-based renormalization method for many-particle Hamiltonians. The method is used to evaluate static and dynamic quantities of the one-dimensional model at half-filling. These include the quasiparticle excitation energy ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}}_{k}$, the momentum distribution nk{n}_{k}nk​ of the conduction electrons, and the spatial correlation functions of the localized electrons. One of the most remarkable results is the appearance of a gap in ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}}_{k}$ at the Fermi level of the order of the Coulomb repulsion UUU, which is accompanied by a smooth behavior for nk{n}_{k}nk​. The density of states for the conduction electrons and the one-particle spectral functions for the localized electrons are also discussed. In both quantities, a gap opens with increasing UUU.
Charge and spin orderings are studied on the simplest one-dimensional (1D) and the two-dimensional (2D) square lattices within the generalized Falicov-Kimball model with Hund coupling between localized and itinerant electrons. Using the restricted phase diagram 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 have been determined. In two dimensions 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 nonmagnetic ones. For band fillings close to the half filling, stripe phases oriented along one of the main diagonal direction are formed. The results suggest the possibility of tuning modulations of charge and magnetic superstructures with a change in doping.
Both canonical and grand canonical phase diagrams of the one dimensional Falicov-Kimball model (FKM) with correlated hopping are presented for several values of the model parameters. Using the method of restricted phase diagrams the system has been studied in the thermodynamic limit. As compare to the conventional FKM, the diagrams exhibit a loss of the particle-hole symmetry. PACS D5.30.Fk, 71.30+h As the simplest, still non-trivial model of highly correlated electron systems, the Falicov-Kimball model (FKM) attracts growing attention among solid state physicists. It can describe variety of the most intriguing cooperative phenomena, as metal-insulator transition, mixed-valence phenomenon etc. (see e.g. the review [1]). The model deals with itinerant particles (electrons) that can hope between nearest-neighbor sites. Some of lattice sites are occupied by non-movable particles, playing a role of ions or localized electrons; we call them ”ions”. The only interaction in the system is the on-site, Coulomb-type interaction between the electrons and the ions. The interaction generates long-range correlations between the ions. The model has been investigated thoroughly in nineties. Numerous approximate results supplemented with some exact and rigorous statements reported up to now provide a good basis for further extensions of the model towards more realistic physical situations. These include the discussed here model with correlated hopping, according to which the electron hopping rate depends on occupations of relevant sites. The Hamiltonian of the FKM with correlated hopping reads:
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 is studied. The flux phase problem where one has to find the optimal flux configurations and the nuclei configurations is also solved in some cases. Finaly 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.