Metal--Insulator Transitions in the Falicov--Kimball Model with Disorder

The ground state phase diagrams of the Falicov--Kimball model with local disorder is derived within the dynamical mean--field theory and using the geometrically averaged (''typical'') local density of states. Correlated metal, Mott insulator and Anderson insulator phases are identified. The metal--insulator transitions are found to be continuous. The interaction and disorder compete with each other stabilizing the metallic phase against occurring one of the insulators. The Mott and Anderson insulators are found to be continuously connected.Comment: 6 pages, 7 figure

Energy versus information based estimations of dissipation using a pair of magnetic colloidal particles

Using the framework of stochastic thermodynamics, we present an experimental study of a doublet of magnetic colloidal particles which is manipulated by a time-dependent magnetic field. Due to hydrodynamic interactions, each bead experiences a state-dependent friction, which we characterize using a hydrodynamic model. In this work, we compare two estimates of the dissipation in this system: the first one is energy based since it relies on the measured interaction potential, while the second one is information based since it uses only the information content of the trajectories. While the latter only offers a lower bound of the former, we find it to be simple to implement and of general applicability to more complex systems.Comment: Main text: 5 pages, 4 figures. Supplementary material: 5 pages, 5 figure

Collective excitation spectrum of a disordered Hubbard model

We study the collective excitation spectrum of a d=3 site-disordered Anderson-Hubbard model at half-filling, via a random-phase approximation (RPA) about broken-symmetry, inhomogeneous unrestricted Hartree-Fock (UHF) ground states. We focus in particular on the density and character of low-frequency collective excitations in the transverse spin channel. In the absence of disorder, these are found to be spin-wave-like for all but very weak interaction strengths, extending down to zero frequency and separated from a Stoner-like band, to which there is a gap. With disorder present, a prominent spin-wave-like band is found to persist over a wide region of the disorder-interaction phase plane in which the mean-field ground state is a disordered antiferromagnet, despite the closure of the UHF single-particle gap. Site resolution of the RPA excitations leads to a microscopic rationalization of the evolution of the spectrum with disorder and interaction strength, and enables the observed localization properties to be interpreted in terms of the fraction of strong local moments and their site-differential distribution.Comment: 25 pages (revtex), 9 postscript figure

Correlated electrons in the presence of disorder

Several new aspects of the subtle interplay between electronic correlations and disorder are reviewed. First, the dynamical mean-field theory (DMFT)together with the geometrically averaged ("typical") local density of states is employed to compute the ground state phase diagram of the Anderson-Hubbard model at half-filling. This non-perturbative approach is sensitive to Anderson localization on the one-particle level and hence can detect correlated metallic, Mott insulating and Anderson insulating phases and can also describe the competition between Anderson localization and antiferromagnetism. Second, we investigate the effect of binary alloy disorder on ferromagnetism in materials with $f$-electrons described by the periodic Anderson model. A drastic enhancement of the Curie temperature $T_c$ caused by an increase of the local $f$-moments in the presence of disordered conduction electrons is discovered and explained.Comment: 17 pages, 7 figures, final version, typos corrected, references updated, submitted to Eur. Phys. J. for publication in the Special Topics volume "Cooperative Phenomena in Solids: Metal-Insulator Transitions and Ordering of Microscopic Degrees of Freedom

Magnetic properties of the three-dimensional Hubbard model at half filling

We study the magnetic properties of the 3d Hubbard model at half-filling in the TPSC formalism, previously developed for the 2d model. We focus on the N\'eel transition approached from the disordered side and on the paramagnetic phase. We find a very good quantitative agreement with Dynamical Mean-Field results for the isotropic 3d model. Calculations on finite size lattices also provide satisfactory comparisons with Monte Carlo results up to the intermediate coupling regime. We point out a qualitative difference between the isotropic 3d case, and the 2d or anisotropic 3d cases for the double occupation factor. Even for this local correlation function, 2d or anisotropic 3d cases are out of reach of DMF: this comes from the inability of DMF to account for antiferromagnetic fluctuations, which are crucial.Comment: RevTex, 9 pages +10 figure

The absence of finite-temperature phase transitions in low-dimensional many-body models: a survey and new results

After a brief discussion of the Bogoliubov inequality and possible generalizations thereof, we present a complete review of results concerning the Mermin-Wagner theorem for various many-body systems, geometries and order parameters. We extend the method to cover magnetic phase transitions in the periodic Anderson Model as well as certain superconducting pairing mechanisms for Hubbard films. The relevance of the Mermin-Wagner theorem to approximations in many-body physics is discussed on a conceptual level.Comment: 33 pages; accepted for publication as a Topical Review in Journal of Physics: Condensed Matte

Magnetic Correlations in the Two Dimensional Anderson-Hubbard Model

The two dimensional Hubbard model in the presence of diagonal and off-diagonal disorder is studied at half filling with a finite temperature quantum Monte Carlo method. Magnetic correlations as well as the electronic compressibility are calculated to determine the behavior of local magnetic moments, the stability of antiferromagnetic long range order (AFLRO), and properties of the disordered phase. The existence of random potentials (diagonal or ``site'' disorder) leads to a suppression of local magnetic moments which eventually destroys AFLRO. Randomness in the hopping elements (off-diagonal disorder), on the other hand, does not significantly reduce the density of local magnetic moments. For this type of disorder, at half-filling, there is no ``sign-problem'' in the simulations as long as the hopping is restricted between neighbor sites on a bipartite lattice. This allows the study of sufficiently large lattices and low temperatures to perform a finite-size scaling analysis. For off-diagonal disorder AFLRO is eventually destroyed when the fluctuations of antiferromagnetic exchange couplings exceed a critical value. The disordered phase close to the transition appears to be incompressible and shows an increase of the uniform susceptibility at low temperatures.Comment: 10 pages, REVTeX, 14 figures included using psfig.st

Insulating phases of the infinite-dimensional Hubbard model

A theory is developed for the T=0 Mott-Hubbard insulating phases of the infinite-dimensional Hubbard model at half-filling, including both the antiferromagnetic (AF) and paramagnetic (P) insulators. Local moments are introduced explicitly from the outset, enabling ready identification of the dominant low energy scales for insulating spin- flip excitations. Dynamical coupling of single-particle processes to the spin-flip excitations leads to a renormalized self-consistent description of the single-particle propagators that is shown to be asymptotically exact in strong coupling, for both the AF and P phases. For the AF case, the resultant theory is applicable over the entire U-range, and is discussed in some detail. For the P phase, we consider in particular the destruction of the Mott insulator, the resultant critical behaviour of which is found to stem inherently from proper inclusion of the spin-flip excitations.Comment: 13 pages Revtex, 12 postscript figure

Disorder-enhanced delocalization and local-moment quenching in a disordered antiferromagnet

The interplay of disorder and spin-fluctuation effects in a disordered antiferromagnet is studied. In the weak-disorder regime (W \le U), while the energy gap decreases rapidly with disorder, the sublattice magnetization, including quantum corrections, is found to remain essentially unchanged in the strong correlation limit. Magnon energies and Neel temperature are enhanced by disorder in this limit. A single paradigm of disorder-enhanced delocalization qualitatively accounts for all these weak disorder effects. Vertex corrections and magnon damping, which appear only at order (W/U)^4, are also studied. With increasing disorder a crossover is found at W \sim U, characterized by a rapid decrease in sublattice magnetization due to quenching of local moments, and formation of spin vacancies. The latter suggests a spin-dilution behavior, which is indeed observed in softened magnon modes, lowering of Neel temperature, and enhanced transverse spin fluctuations.Comment: 12 pages, includes 8 postscript figures. To appear in Physical Review B. References adde

Disorder and Impurities in Hubbard-Antiferromagnets

We study the influence of disorder and randomly distributed impurities on the properties of correlated antiferromagnets. To this end the Hubbard model with (i) random potentials, (ii) random hopping elements, and (iii) randomly distributed values of interaction is treated using quantum Monte Carlo and dynamical mean-field theory. In cases (i) and (iii) weak disorder can lead to an enhancement of antiferromagnetic (AF) order: in case (i) by a disorder-induced delocalization, in case (iii) by binding of free carriers at the impurities. For strong disorder or large impurity concentration antiferromagnetism is eventually destroyed. Random hopping leaves the local moment stable but AF order is suppressed by local singlet formation. Random potentials induce impurity states within the charge gap until it eventually closes. Impurities with weak interaction values shift the Hubbard gap to a density off half-filling. In both cases an antiferromagnetic phase without charge gap is observed.Comment: 16 pages, 9 figures, latex using vieweg.sty (enclosed); typos corrected, references updated; to appear in "Advances in Solid State Physics", Vol. 3