Anderson-Hubbard Model Research Articles

Resistivity characteristics near the metal–insulator transition in the half-filled Anderson–Hubbard model

Resistivity characteristics near the metal–insulator transition in the half-filled Anderson–Hubbard model

Phase diagram of the half-filled Anderson-Hubbard model at finite temperature

We study metal-insulator phase diagram in the half-filled disordered Hubbard model at finite temperature. We calculate the averaged local density of states at the Fermi level and the site occupation as a function of the on-site energy at finite temperature by using typical medium theory with an impurity solver of equation of motion method. Although the metallicity in the correlated metallic region changes with temperature change, the phase diagram is almost temperature independent. We find fairly good agreement between our site occupation and those obtained by the typical medium method with other impurity solver.

Nonequilibrium DMFT+CPA for correlated disordered systems

We present a solution for the nonequilibrium dynamics of an interacting disordered system. The approach adapts the combination of the equilibrium dynamical mean-field theory and the equilibrium coherent potential approximation methods to the nonequilibrium many-body formalism, using the Kadanoff-Baym-Keldysh complex time contour, for the dynamics of interacting disordered systems away from equilibrium. We use our time domain solution to obtain the equilibrium density of states of the disordered interacting system described by the Anderson-Hubbard model, bypassing the necessity for the cumbersome analytical continuation process. We further apply the nonequilibrium solution to the interaction quench problem for an isolated disordered system. Here, the interaction is abruptly changed from zero (noninteracting system) to another constant (finite) value at which it is subsequently kept. We observe via the time dependence of the potential, kinetic, and total energies the effect of disorder on the relaxation of the system as a function of final interaction strength. The real-time approach has the potential to shed light on the fundamental role of disorder in the nonequilibrium dynamics of interacting quantum systems.

Machine learning predictions for local electronic properties of disordered correlated electron systems

We present a scalable machine learning (ML) model to predict local electronic properties such as on-site electron number and double occupation for disordered correlated electron systems. Our approach is based on the locality principle, or the nearsightedness nature, of many-electron systems, which means local electronic properties depend mainly on the immediate environment. A ML model is developed to encode this complex dependence of local quantities on the neighborhood. We demonstrate our approach using the square-lattice Anderson-Hubbard model, which is a paradigmatic system for studying the interplay between Mott transition and Anderson localization. We develop a lattice descriptor based on group-theoretical method to represent the on-site random potentials within a finite region. The resultant feature variables are used as input to a multi-layer fully connected neural network, which is trained from datasets of variational Monte Carlo (VMC) simulations on small systems. We show that the ML predictions agree reasonably well with the VMC data. Our work underscores the promising potential of ML methods for multi-scale modeling of correlated electron systems.

Strongly correlated zero-bias anomaly in double quantum dot measurements

Experiments in doped transition metal oxides often show suppression in the single-particle density of states at the Fermi level, but disorder-induced zero-bias anomalies in strongly correlated systems remain poorly understood. Numerical studies of the Anderson-Hubbard model have identified a zero-bias anomaly that is unique to strongly correlated materials, with a width proportional to the intersite hopping amplitude t [S. Chiesa, P. B. Chakraborty, W. E. Pickett, and R. T. Scalettar, Phys. Rev. Lett. 101, 086401 (2008)]. In ensembles of two-site systems, a zero-bias anomaly with the same parameter dependence also occurs, suggesting a similar physical origin [R. Wortis and W. A. Atkinson, Phys. Rev. B 82, 073107 (2010)]. We describe how this kinetic-energy-driven zero-bias anomaly in ensembles of two-site systems may be seen in a mesoscopic realization based on double quantum dots. Moreover, the double-quantum-dot measurements provide access not only to the ensemble-average density of states but also to the details of the transitions which give rise to the zero-bias anomaly.

Anderson localization in the Anderson–Hubbard model with site-dependent interactions

We consider Anderson localization in the half-filled Anderson–Hubbard model in the presence of either random on-site interactions or spatially alternating interactions in the lattice. By using dynamical mean field theory with the equation of motion method as an impurity solver, we calculate the arithmetically and geometrically averaged local density of states and derive the equations determining the critical value for the phase transition between metallic, Anderson and Mott insulating phases. The nonmagnetic ground state phase diagrams are constructed numerically. We figure out that the presence of Coulomb disorder drives the system toward the Anderson localized phase that can occur even in the absence of Anderson structural disorder. For the spatially alternating interactions, we find that the metallic region is reduced and the Anderson insulator one is enlarged with increasing interaction modulation. Our obtained results are relevant to current research in ultracold atoms in disordered optical lattices where metal–insulator transition can be observed experimentally by using ultracold atom techniques.

Dynamical mean-field theory of the Anderson-Hubbard model with local and nonlocal disorder in tensor formulation

To explore correlated electrons in the presence of local and non-local disorder, the Blackman-Esterling-Berk method for averaging over off-diagonal disorder is implemented into dynamical mean-field theory using tensor notation. The impurity model combining disorder and correlations is solved using the recently developed fork tensor-product state solver, which allows one to calculate the single particle spectral functions on the real-frequency axis. In the absence of off-diagonal hopping, we establish exact bounds of the spectral function of the non-interacting Bethe lattice with coordination number $Z$. In the presence of interaction, the Mott insulating paramagnetic phase of the one-band Hubbard model is computed at zero temperature in alloys with site- and off-diagonal disorder. When the Hubbard $U$ parameter is increased, transitions from an alloy band-insulator through a correlated metal into a Mott insulating phase are found to take place.

Metal–insulator transitions of fermionic mixtures with mass imbalance in disordered optical lattice

We study the metal–insulator transitions in the half-filled Anderson–Hubbard model with mass imbalance by the typical medium theory using the equation of motion method as an impurity solver. The nonmagnetic ground state phase diagram of the system with mass imbalance is constructed numerically. In addition to the three phases showed up in the balanced case, the phase diagram of the mass imbalanced case contains a spin-selective localized phase, where one spin component is metallic while the other spin component is insulating. We find that if one increases the mass imbalance the metal region in the phase diagram is reduced, while both Anderson and Mott insulator regions are enlarged.

Two-body metal-insulator transitions in the Anderson-Hubbard model

We review our recent results on Anderson localization in systems of two interacting particles coupled by contact interactions. Based on an exact mapping to an effective single-particle problem, we numerically investigate the occurrence of metal-insulator phase transitions for the pair in two-(2D) and three-dimensional (3D) disordered lattices. In two dimensions, we find that interactions cause an exponential enhancement of the pair localization length with respect to its single-particle counterpart, but do not induce a delocalization transition. In particular we show that previous claims of 2D interaction-induced Anderson transitions are the results of strong finite-size effects. In three dimensions we find that the pair undergoes a metal-insulator transition belonging to the same (orthogonal) universality class of the noninteracting model. We then explore the phase diagram in the space of energy E, disorder W and interaction strength U, which reveals a rich and counterintuitive structure, endowed with multiple metallic and insulating phases. We point out that this phenomenon originates from the molecular and scattering-like nature of the pair states available at given energy and disorder strength.

Absence of two-body delocalization transitions in the two-dimensional Anderson-Hubbard model

We investigate Anderson localization of two particles moving in a two-dimensional (2D) disordered lattice and coupled by contact interactions. Based on transmission-amplitude calculations for relatively large strip-shaped grids, we find that all pair states are localized in lattices of infinite size. In particular, we show that previous claims of an interaction-induced mobility edge are biased by severe finite-size effects. The localization length of a pair with zero total energy exhibits a nonmonotonic behavior as a function of the interaction strength, characterized by an exponential enhancement in the weakly interacting regime. Our findings also suggest that the many-body mobility edge of the 2D Anderson-Hubbard model disappears in the zero-density limit, irrespective of the (bosonic or fermionic) quantum statistics of the particles.

Two-body mobility edge in the Anderson-Hubbard model in three dimensions: Molecular versus scattering states

Most of our quantitative understanding of disorder-induced metal-insulator transitions comes from numerical studies of simple noninteracting tight-binding models, like the Anderson model in three dimensions. An important outstanding problem is the fate of the Anderson transition in the presence of additional Hubbard interactions of strength $U$ between particles. Based on large-scale numerics, we compute the position of the mobility edge for a system of two identical bosons or two fermions with opposite spin components. The resulting phase diagram in the interaction-energy-disorder space possesses a remarkably rich and counterintuitive structure, with multiple metallic and insulating phases. We show that this phenomenon originates from the molecular or scattering-like nature of the pair states available at given energy $E$ and disorder strength $W$. The disorder-averaged density of states of the effective model for the pair is also investigated. Finally, we discuss the implications of our results for ongoing research on many-body localization.

Effect of Isomorphic Impurities on the Elastic Conductivity of Chiral Carbon Nanotubes

A theoretical study is made of the piezoresistive properties of chiral carbon nanotubes with different types of conduction, both ideal and doped with substitutional point defects at different concentrations, uniformly distributed in the crystal lattice. Boron and nitrogen atoms are chosen as acceptor and donor impurities, respectively. The energy-band structure of the studied nanoparticles is examined using the Hubbard–Anderson model and Green’s function. The longitudinal component of the tensor of elastic conductivity is calculated analytically, and the dependence of this tensor on the diameter of nanotubes, the relative longitudinal compressive and tensile deformations, and the concentration of impurities are studied. The obtained results are validated physically and compared to the literature data.

Self-energy Padé approach for analytic continuation: Application to the zero-gap Kondo lattice model

A modified Pade approach is presented as analytic continuation for numerical methods that evaluate correlation functions in imaginary time. Instead of the direct analytic continuation of the correlation functions, the Pade method is applied for the self-energy that is then used for deriving the Green's functions at real energies. We find that this modified, self-energy Pade approach is more stable and robust against statistical errors compared to the direct way. The characteristics and success of the modified Pade approach are analyzed by actual calculations for the illustrative cases of the non-interacting Anderson lattice and Hubbard model. A zero-gap Kondo lattice model with linearly vanishing conduction electron density of states at the Fermi level is also studied, where we use the modified Pade approach as analytic continuation. We investigate the properties of the Kondo insulating state including the dependence of the insulating gap on the Kondo coupling and coherence effects. Furthermore, we identify two energy scales from dynamic and thermodynamic quantities, that are associated as a direct and an indirect gap in a band hybridization picture.

Zero bias anomaly in the two-site Anderson-Hubbard model with Gaussian distribution for disorder

The Anderson-Hubbard model considers the correlation between disorder and other interactions in a strongly correlated electron system. Both disorder and correlations drive the metal-insulator transition but the densities of states behave in different ways. The zero bias anomaly (ZBA) referring to the V-dip shape of the density of states at the Fermi energy occurs in the strong disorder and strong interaction regime instead of a hard Coulomb gap in an insulator phase of strongly correlated interacting systems. In this paper, we use a Gaussian distribution for disorder to examine a two-site Anderson-Hubbard model. We also explain comprehensively the relationship between the phase diagram of ground states with various numbers of electrons and the behavior of the density of states. Furthermore, we want to investigate the effect of disorder distribution on the formation of the ZBA which originates from a hopping mechanism in two specific configurations.

Impurity band magnetism in organic semiconductors

Recent experiments and theoretical studies have proposed that spin-transport in organic semiconductors, in particular in ${\mathrm{Alq}}_{3}$, may occur in an impurity band. Here we model the electronic and magnetic properties of such an impurity band by treating the effect of disorder in a numerically accurate way. The calculations are carried out by solving the Anderson-Hubbard model within the mean-field approximation and by accounting for magnetic excitations via the Bethe-Salpeter equation. We find that some impurities form clusters where electrons are delocalized, while others develop localized magnetic moments, which are antiferromagnetically correlated. The excitations of these correlated magnetic moments are spin waves, which can enable spin transport.

Machine learning electron correlation in a disordered medium

Learning from data has led to a paradigm shift in computational materials science. In particular, it has been shown that neural networks can learn the potential energy surface and interatomic forces through examples, thus bypassing the computationally expensive density functional theory calculations. Combining many-body techniques with a deep-learning approach, we demonstrate that a fully connected neural network is able to learn the complex collective behavior of electrons in strongly correlated systems. Specifically, we consider the Anderson-Hubbard (AH) model, which is a canonical system for studying the interplay between electron correlation and strong localization. The ground states of the AH model on a square lattice are obtained using the real-space Gutzwiller method. The obtained solutions are used to train a multitask multilayer neural network, which subsequently can accurately predict quantities such as the local probability of double occupation and the quasiparticle weight, given the disorder potential in the neighborhood as the input.

Emergence of non-Fermi liquid dynamics through nonlocal correlations in an interacting disordered system

We provide strong evidence of a quantum critical point (QCP) associated with the destruction of Kondo screening in the Anderson-Hubbard model for interacting electrons with quenched disorder. A unique crossover energy scale, $\omega^*$ separating the Fermi liquid and non-Fermi liquid (nFL) scattering dynamics on the metallic side of the quantum critical fan is identified. The scale vanishes at the disorder driven QCP. We interpret our results by measuring the distribution of Kondo scales and find that the QCP occurs when this distribution acquires a finite intercept, indicating a Kondo destruction scenario, albeit distinct from the local QCP picture. The nFL behavior is shown to stem from an interplay of strong electron-electron interactions and the systematic inclusion of short-range dynamical fluctuations induced by the underlying random potential. The results have been obtained through a computational framework based on the typical medium dynamical cluster approximation.

Effect of atomic disorder on the magnetic phase separation

The effect of disorder on the magnetic phase separation between the antiferromagnetic and incommensurate helical and phases is investigated. The study is based on the quasi-two-dimensional single-band Hubbard model in the presence of atomic disorder (the Anderson–Hubbard model). A model of binary alloy disorder is considered, in which the disorder is determined by the difference in energy between the host and impurity atomic levels at a fixed impurity concentration. The problem is solved within the theory of functional integration in static approximation. Magnetic phase diagrams are obtained as functions of the temperature, the number of electrons and impurity concentration with allowance for phase separation. It is shown that for the model parameters chosen, the disorder caused by impurities whose atomic-level energy is greater than that of the host atomic levels, leads to qualitative changes in the phase diagram of the impurity-free system. In the opposite case, only quantitative changes occur. The peculiarities of the effect of disorder on the phase separation regions of the quasi-two-dimensional Hubbard model are discussed.

Local integrals of motion in the two-site Anderson-Hubbard model

It has been proposed that the states of fully many-body localized systems can be described in terms of conserved local pseudospins. Due to the multitude of ways to define these, the explicit identification of the optimally local pseudospins in specific systems is non-trivial. Given continuing intense interest in the role of disorder in strongly correlated systems, we consider the disordered Hubbard model. By studying a small system we provide concrete examples of the form of local integrals of motion in the Anderson-Hubbard model. Moreover, we are able not only to identify the most local choice but also to explore the nature of the distribution of possible choices. We track the evolution of the optimally localized pseudospins as hopping and interactions are varied to move the system away from the trivially localized atomic limit.

Non-Fermi Liquid Behavior and Continuously Tunable Resistivity Exponents in the Anderson-Hubbard Model at Finite Temperature.

We employ a recently developed computational many-body technique to study for the first time the half-filled Anderson-Hubbard model at finite temperature and arbitrary correlation U and disorder V strengths. Interestingly, the narrow zero temperature metallic range induced by disorder from the Mott insulator expands with increasing temperature in a manner resembling a quantum critical point. Our study of the resistivity temperature scaling T^{α} for this metal reveals non-Fermi liquid characteristics. Moreover, a continuous dependence of α on U and V from linear to nearly quadratic is observed. We argue that these exotic results arise from a systematic change with U and V of the "effective" disorder, a combination of quenched disorder and intrinsic localized spins.