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

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 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

Artificial Intelligence and Liver Transplant:Predicting Survival of Individual Grafts

The demand for liver transplantation far outstrips the supply of deceased donor organs, and so, listing and allocation decisions aim to maximize utility. Most existing methods for predicting transplant outcomes use basic methods, such as regression modeling, but newer artificial intelligence (AI) techniques have the potential to improve predictive accuracy. The aim was to perform a systematic review of studies predicting graft outcomes following deceased donor liver transplantation using AI techniques and to compare these findings to linear regression and standard predictive modeling: donor risk index (DRI), Model for End‐Stage Liver Disease (MELD), and Survival Outcome Following Liver Transplantation (SOFT). After reviewing available article databases, a total of 52 articles were reviewed for inclusion. Of these articles, 9 met the inclusion criteria, which reported outcomes from 18,771 liver transplants. Artificial neural networks (ANNs) were the most commonly used methodology, being reported in 7 studies. Only 2 studies directly compared machine learning (ML) techniques to liver scoring modalities (i.e., DRI, SOFT, and balance of risk [BAR]). Both studies showed better prediction of individual organ survival with the optimal ANN model, reporting an area under the receiver operating characteristic curve (AUROC) 0.82 compared with BAR (0.62) and SOFT (0.57), and the other ANN model gave an AUC ROC of 0.84 compared with a DRI (0.68) and SOFT (0.64). AI techniques can provide high accuracy in predicting graft survival based on donors and recipient variables. When compared with the standard techniques, AI methods are dynamic and are able to be trained and validated within every population. However, the high accuracy of AI may come at a cost of losing explainability (to patients and clinicians) on how the technology works

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

Constrained-path quantum Monte Carlo simulations of the zero-temperature disordered two-dimensional Hubbard model

We study the effects of disorder on long-range antiferromagnetic correlations in the half-filled, two dimensional, repulsive Hubbard model at T=0. A mean field approach is first employed to gain a qualitative picture of the physics and to guide our choice for a trial wave function in a constrained path quantum Monte Carlo (CPQMC) method that allows for a more accurate treatment of correlations. Within the mean field calculation, we observe both Anderson and Mott insulating antiferromagnetic phases. There are transitions to a paramagnet only for relatively weak coupling, U < 2t in the case of bond disorder, and U < 4t in the case of on-site disorder. Using ground-state CPQMC we demonstrate that this mean field approach significantly overestimates magnetic order. For U=4t, we find a critical bond disorder of Vc = (1.6 +- 0.4)t even though within mean field theory no paramagnetic phase is found for this value of the interaction. In the site disordered case, we find a critical disorder of Vc = (5.0 +- 0.5)t at U=4t.Comment: Revtex, 13 pages, 15 figures. Minor changes to title and abstract, discussion and references added, figures 5, 6, 8, 9 replaced with easier to read version