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.
The phase diagram of correlated, disordered electrons is calculated within dynamical mean--field theory using the geometrically averaged (''typical'') local density of states. Correlated metal, Mott insulator and Anderson insulator phases, as well as coexistence and crossover regimes are identified. The Mott and Anderson insulators are found to be continuously connected.
A two-band model of a disordered semiconductor is used to analyze dynamical interaction induced weakening of localization in a system that is accessible to experimental verification. The results show a dependence on the sign of the two-particle interaction and on the optical excitation energy of the Coulomb-correlated electron-hole pair.
We report exact multielectronic ground-states dependent on electron concentration for quantum mechanical two-dimensional disordered two-band type many body models in the presence of disordered hoppings and disordered repulsive finite Hubbard interactions, in fixed lattice topology considered provided by Bravais lattices. The obtained ground-states loose their eigenfunction character for independent electron approximation, perturbatively are not connected to the non-interacting but disordered case, and describe a localization-delocalization transition driven by the electron concentration, being…
Temperature dependent transport of disordered electronic systems is examined in the presence of strong correlations. In contrast to what is assumed in Fermi liquid approaches, finite temperature behavior in this regime proves largely dominated by inelastic electron-electron scattering. This conclusion is valid in the strong coupling limit, where the disorder, the correlations and the Fermi energy are all comparable, as in many materials near the metal-insulator transition.
We develop a novel quantum transfer matrix method to study thermodynamic properties of one-dimensional (1D) disordered electronic systems. It is shown that the partition function can be expressed as a product of $2\times2$ local transfer matrices. We demonstrate this method by applying it to the 1D disordered Anderson model. Thermodynamic quantities of this model are calculated and discussed.
While the coherent potential approximation (CPA) is the prevalent method for the study of disordered electronic systems, it fails to capture non-local correlations and Anderson localization. To incorporate such effects, we extend the dual fermion approach to disordered non-interacting systems using the replica method. Results for single- and two- particle quantities show good agreement with cluster extensions of the CPA; moreover, weak localization is captured. As a natural extension of the CPA, our method presents an alternative to the existing cluster theories. It can be used in various appl…
We present here a theoretical model in order to describe the competition between the Kondo effect and the spin glass behavior. The spin glass part of the starting Hamiltonian contains Ising spins with an intersite exchange interaction given by the local van Hemmen model, while the Kondo effect is described as usual by the intrasite exchange $J_K$. We obtain, for large $J_K$ values, a Kondo phase and, for smaller $J_K$ values, a succession, with decreasing
Combining the self-consistent theory of localization and the dynamical mean-field theory, we present a theoretical approach capable of describing both self-trapping of charge carriers during the process of polaron formation and disorder-induced Anderson localization. By constructing random samples for the local density of states (LDOS) we analyze the distribution function for this quantity and demonstrate that the typical rather than the mean LDOS is a natural measure to distinguish between itinerant and localized states. Significant polaron effects on the mobility edge are found.
We calculate the dynamic effective electron-electron interaction potential for a low density disordered two-dimensional electron gas. The disordered response function is used to calculate the effective potential where the scattering rate is taken from typical mobilities from recent experiments. We investigate the development of an effective attractive pair potential for both disordered and disorder free systems with correlations determined from existing numerical simulation data. The effect of disorder and correlations on the superconducting critical temperature Tc is discussed.
An ensemble of 2d disordered clusters with a few electrons is studied as a function of the Coulomb energy to kinetic energy ratio r_s. Between the Fermi system (small r_s) and the Wigner molecule (large r_s), an interaction induced delocalization of the ground state takes place which is suppressed when the spins are aligned by a parallel magnetic field. Our results confirm the existence of an intermediate regime where the Wigner antiferromagnetism defavors the Stoner ferromagnetism and where the enhancement of the Lande g factor observed in dilute electron systems is reproduced.
We present a unified, global perspective on the magnetic properties of strongly disordered electronic systems, with special emphasis on the case where the ground state is metallic. We review the arguments for the instability of the disordered Fermi liquid state towards the formation of local magnetic moments, and argue that their singular low temperature thermodynamics are the ``quantum Griffiths'' precursors of the quantum phase transition to a metallic spin glass; the local moment formation is therefore not directly related to the metal-insulator transition. We also review the the mean-field…
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 (DMFT) and the equilibrium coherent potential approximation (CPA) 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…
We study the low temperature transport characteristics of a disordered metal in the presence of electron-electron interactions. We compare Hartree-Fock and dynamical mean field theory (DMFT) calculations to investigate the scattering processes of quasiparticles off the screened disorder potential and show that both the local and non-local (coming from long-ranged Friedel oscillations) contributions to the renormalized disorder potential are suppressed in strongly renormalized Fermi liquids. Our results provide one more example of the power of DMFT to include higher order terms left out by weak…
There is a common belief in the condensed matter community that bulk quantities become insensitive to the boundary condition in the infinite-volume limit. Here we reconsider this statement in terms of recent arguments of non-Hermitian skin effects, -strong dependence of spectra on boundary conditions for the non-Hermitian Hamiltonians-, in the traditional Green's function formalism. We find the criterion for quantities to be sensitive/insensitive against the boundary condition in Hermitian correlated/disordered systems, which is characterized by the residue theorem. We also discuss the uncerta…
Besides a drastic reduction in saturation magnetization of disordered Sr2FeMoO6 compared to highly ordered samples, magnetizations as a function of the temperature for different disordered samples may also show qualitatively different behaviors. We investigate the origin of such diversity by performing spatially resolved photoemission spectroscopy on various disordered samples. Our results establish that extensive electronic inhomogeneity, arising most probably from an underlying chemical inhomogeneity in disordered samples is responsible for the observed magnetic inhomogeneity. It is further …
We investigate the metal insulator transitions at finite temperature for the Hubbard model with diagonal alloy disorder. We solve the dynamical mean field theory equations with the non crossing approximation and we use the coherent potential approximation to handle disorder. The excitation spectrum is given for various correlation strength $U$ and disorder. Two successive metal insulator transitions are observed at integer filling values as $U$ is increased. An important selective transfer of spectral weight arises upon doping. The strong influence of the temperature on the low energy dynamics…
We investigate the effects of randomness in a strongly correlated electron model in one-dimension at half-filling. The ground state correlation functions are exactly written by products of 3$\times$3 transfer matrices and are evaluated numerically. The correlation lengths depend on randomness when the interaction is effectively weak. On the contrary, they are completely insensitive to randomness when the interaction is effectively strong.
We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. Two alternative approaches to the problem are developed, both combining fermionic and bosonic treatment of the underlying physics. We calculate the relevant dephasing rate, which for spinless electrons is governed by the interplay of electron-electron interaction and disorder, thus vanishing in the clean limit. Our approach provides…
Disordered 2D chiral fermions provide an effective description of several materials including graphene and topological insulators. While previous analysis considered delta correlated disorder and no ultraviolet cut-offs, we consider here the effect of short range correlated disorder and the presence of a momentum cut-off, providing a more realistic description of condensed matter models. We show that the density of states is anomalous with a critical exponent function of the disorder and that conductivity is universal only when the ultraviolet cut-off is removed, as consequence of the supersym…
Local ultrafast optical excitation of electron-hole pairs in disordered semiconductors provides the possibility to observe experimentally interaction-assisted propagation of correlated quantum particles in a disordered environment. In addition to the interaction driven delocalization known for the conventional single-band TIP-(two-interacting-particles)-problem the semiconductor model has a richer variety of physical parameters that give rise to new features in the temporal dynamics. These include different masses, correlated vs. anticorrelated disorder for the two particles, and dependence on…
We investigate electron transport in disordered Hubbard chains contacted to macroscopic leads, via the non-equilibrium Green's functions technique. We observe a cross-over of currents and conductances at finite bias which depends on the relative strength of disorder and interactions. The finite-size scaling of the conductance is highly dependent on the interaction strength, and exponential attenuation is not always seen. We provide a proof that the Coherent Potential Approximation, a widely used method for treating disorder averages, fulfils particle conservation at finite bias with or without…
For many years the Korringa-Kohn-Rostoker coherent-potential approximation (KKR-CPA) has been widely used to describe the electronic structure of disordered systems based upon a first-principles description of the crystal potential. However, as a single-site theory the KKR-CPA is unable to account for important environmental effects such as short-range order (SRO) in alloys and spin fluctuations in magnets, amongst others. Using the recently devised KKR-NLCPA (where NL stands for nonlocal), we show how to remedy this by presenting explicit calculations for the effects of SRO on the electronic …
We extend the single-site coherent potential approximation (CPA) to include the effects of non-local disorder correlations (alloy short-range order) on the electronic structure of random alloy systems. This is achieved by mapping the original Anderson disorder problem to that of a selfconsistently embedded cluster. This cluster problem is then solved using the equations of motion technique. The CPA is recovered for cluster size $N_{c}=1$, and the disorder averaged density-of-states (DOS) is always positive definite. Various new features, compared to those observed in CPA, and related to repeat…
We study the dimensional dependence of the interplay between correlation and disorder in two dimension at half filling using 2D $t-t'$ disordered Hubbard model with deterministic disorder both at zero and finite temperatures. Inclusion of $t'$ without disorder leads to a metallic phase at half filling below a certain critical value of $U$. Above this critical value $U_c$ correlation favours antiferromagnetic phase. Since disorder leads to double occupancy over the lower energy site, the competition between Hubbard $U$ and disorder leads to the emergence of a metallic phase, which can be quanti…
We present a theory of the metal-insulator transition in a disordered two-dimensional electron gas. A quantum critical point, separating the metallic phase which is stabilized by electronic interactions, from the insulating phase where disorder prevails over the electronic interactions, has been identified. The existence of the quantum critical point leads to a divergence in the density of states of the underlying collective modes at the transition, causing the thermodynamic properties to behave critically as the transition is approached. We show that the interplay of electron-electron interac…
We calculate electronic single-particle properties of short-range ordered stripe states, using Monte-Carlo simulations of collective charge-density wave (CDW) order parameters coupled to fermions on a 2d square lattice. For superconducting bond-centered stripes with a d-wave form factor, we find a valence-bond "glass" which coexists with low-energy quasiparticles featuring interference phenomena, in agreement with recent scanning-tunneling-microscopy (STM) measurements on underdoped BSCCO and CaNaCuOCl. Together with earlier work, our calculations provide a link between CDW features seen in ST…
We study a one-dimensional system of spinless electrons in the presence of a long-range Coulomb interaction (LRCI) and a random chemical potential at each site. We first present a Tomonaga-Luttinger liquid (TLL) description of the system. We use the bosonization technique followed by the replica trick to average over the quenched randomness. An expression for the localization length of the system is then obtained using the renormalization group method and also a physical argument. We then find the density of states for different values of the energy; we get different expressions depending on w…
We performed measurements at helium temperatures of the electronic transport in an InAs quantum wire ($R_{wire} \sim 30$\,k$Ω$) in the presence of a charged tip of an atomic force microscope serving as a mobile gate. The period and the amplitude of the observed quasiperiodic oscillations are investigated in detail as a function of electron concentration in the linear and non-linear regime. We demonstrate the influence of the tip-to-sample distance on the ability to locally affect the top subband electrons as well as the electrons in the disordered sea. Furthermore, we introduce a new method of…
More than fifty years old "Anderson's theorem" suggests disorder-independent pair-amplitude and critical temperature at low to moderate strength of disorders. In spite of the extension of this paradigm and several subsequent theoretical proposals, mechanism for the superconductor-insulator transition (SIT) at large disorder is still an open problem. The understanding of experimental data at intermediate disorder is also lacking. Here, we proceed beyond "Anderson's theorem" by calculating disorder-averaged two-point pair-amplitude fluctuations. We find this correlation to be finite and long-ran…
We numerically investigate the transport properties of disordered interacting electrons in three dimensions in the metallic as well as in the insulating phases. The disordered many-particle problem is modeled by the quantum Coulomb glass which contains a random potential, long-range unscreened Coulomb interactions and quantum hopping between different sites. We have recently developed the Hartree-Fock based diagonalization (HFD) method which amounts to diagonalizing the Hamiltonian in a suitably chosen energetically truncated basis. This method allows us to investigate comparatively large syst…
It is well known that translational symmetry-breaking disorder will disrupt ARPES spectra up to the point where they become invisible. However, a theoretical framework to capture this phenomenon has been largely missing. Here, based on a rigorous theory of the ARPES process, we provide this much-needed framework. In particular, we show how the frequently used sudden electron approximation has to be modified in this situation. Our main result is an argument that links the photoemission line broadening with an operator content of a disorder operator and so with the criticality of the correspondi…
Two powerful theoretical predictions, Anderson localization and the Imry-Ma argument, impose significant restrictions on the phases of matter that can exist in the presence of even the smallest amount of disorder in one-dimensional systems. These predictions forbid conducting states and ordered states respectively. It was thus remarkable that a mechanism to circumvent Anderson localization relying on the presence of correlated disorder was found, that is also realized in certain biomolecular systems. In a similar manner, we show that the Imry-Ma argument can be circumvented resulting in the fo…
Hybrid quantum-classical matrix-product state and Lanczos methods for electron-phonon systems with strong electronic correlations: Application to disordered systems coupled to Einstein phonons
Georg-August-Universität Göttingen（哥廷根大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
We study the effect of disorder on the semimetal -- Mott insulator transition in the half-filled repulsive Hubbard model on a honeycomb lattice, a system that features vanishing density of states at the Fermi level. Using the determinant quantum Monte Carlo method, we characterize various phases in terms of the bulk-limit antiferromagnetic (AF) order parameter, compressibility, and temperature-dependent DC conductivity. In the clean limit, our data are consistent with previous results showing a single quantum critical point separating the semi-metallic and AF Mott insulating phases. With the p…
We study the ground state phase diagram of the Anderson-Hubbard model with correlated hopping at half filling in one-dimension. The Hamiltonian has a local Coulomb repulsion $U$ and a disorder potential with local energies randomly distributed in the interval $(-W,+W)$ with equal probability, acting on the singly occupied sites. The hopping process which modifies the number of doubly occupied sites is forbidden. The hopping between nearest-neighbor singly occupied and empty sites or between singly occupied and doubly occupied sites have the same amplitude $t$. We identify three different phase…
The persistent current is here studied in one-dimensional disordered rings that contain interacting electrons. We used the density matrix renormalization group algorithms in order to compute the stiffness, a measure that gives the magnitude of the persistent currents as a function of the boundary conditions for different sets of both interaction and disorder characteristics. In contrast to its non-interacting value, an increase in the stiffness parameter was observed for systems at and off half-filling for weak interactions and non-zero disorders. Within the strong interaction limit, the decre…
Recently, there has been a resurgence of intense experimental and theoretical interest on the Kondo physics of nanoscopic and mesoscopic systems due to the possibility of making experiments in extremely small samples. We have carried out exact diagonalization calculations to study the effect of energy spacing $Δ$ in the conduction band states, hybridization, number of electrons, and disorder on the ground-state and thermal properties of strongly-correlated electron nanoclusters. For the ordered systems, the calculations reveal for the first time that $Δ$ tunes the interplay between the {\it lo…
We present and discuss an original method to synthesize disordered Nanostructured (NS) VO$_x$ films with controlled stoichiometry and tunable electronic structures. In these NS films, the original lattice symmetry of the bulk vanadium oxides is broken and atoms are arranged in a highly disordered structure . The stoichiometry-dependent disorder as a function of the oxygen concentration has been characterized by in-situ X-ray Absorption Near-Edge Structure (XANES) spectroscopy identifying the spectroscopic fingerprints. Results show structural rearrangements that deviate from the octahedral sym…
Many-body interactions in effective field theories for disordered interacting electrons are considered. It is shown that three-body and higher interaction terms are generated in perturbation theory, and some of the physical consequences of these interactions are discussed. It is shown in particular that they will in general be important for any effects governed by strong-coupling fixed points. This implies that the usual generalized nonlinear sigma-model for disordered electron systems is incomplete, and not suitable for studying strong-coupling effects.
We comment on article by Yi Zhang , Hanna Terletska, Ka-Ming Tam, Yang Wang, Markus Eisenbach, Liviu Chioncel, and Mark Jarrell [Phys. Rev. B {\bf 100}, 054205 (2019)]\cite{Zhang} in which to study substitution disordered systems, they presented an embedding scheme for the locally self-consistent method. Here we show that their methods is a truncated case of our super-cell approximation, achieved by neglecting super-cell wave vectors dependence on self-energy $Σ_{sc}({\bf K}_{n},E)$ and replacing them by a local on-site self-energy, $Σ_{sc}({\bf K}_{n},E)=Σ_{sc}(L,L,E)$ in our articles\cite{Mo…
We demonstrate that a distinct high-disorder anomalous Hall effect phase emerges at the correlated insulator threshold of ultra-thin, amorphous, ferromagnetic CNi3 films. In the weak localization regime, where the sheet conductance G >> e^2/h, the anomalous Hall resistance of the films increases with increasing disorder and the Hall conductance scales as Gxy ~ G^1.6. However, at sufficiently high disorder the system begins to enter the 2D correlated insulator regime, at which point the Hall resistance Rxy abruptly saturates and the scaling exponent becomes 2. Tunneling measurements show that t…
Weyl semimetals have been intensely studied as a three dimensional realization of a Dirac-like excitation spectrum where the conduction bands and valence bands touch at isolated Weyl points in momentum space. Like in graphene, this property entails various peculiar electronic properties. However, recent theoretical studies have suggested that resonant scattering from rare regions can give rise to a non-zero density of states even at charge neutrality. Here, we give a detailed account of this effect and demonstrate how the semimetallic nature is suppressed at the lowest scales. To this end, we …
A diagrammatic method is applied to study the effects of commensurability in two-dimensional disordered crystalline metals by using the particle-hole symmetry with respect to the nesting vector P_0={\pmπ/a, π/a} for a half-filled electronic band. The density of electronic states (DoS) is shown to have nontrivial quantum corrections due to both nesting and elastic impurity scattering processes, as a result the van Hove singularity is preserved in the center of the band. However, the energy dependence of the DoS is strongly changed. A small offset from the middle of the band gives rise to disapp…
Using the Lindblad equation approach, we derive the range of the parameters of an interacting one-dimensional electronic chain connected to two reservoirs in the large bias limit in which an optimal working point (corresponding to a change in the monotonicity of the stationary current as a function of the applied bias) emerges in the nonequilibrium stationary state. In the specific case of the one-dimensional spinless fermionic Hubbard chain, we prove that an optimal working point emerges in the dependence of the stationary current on the coupling between the chain and the reservoirs, both in …
For heterostructures of ultrathin, strongly correlated copper-oxide films and dielectric perovskite layers, we predict inhomogeneous electronic interface states. Our study is based on an extended Hubbard model for the cuprate film. The interface is implemented by a coupling to the electron and phonon degrees of freedom of the dielectric oxide layer. We find that electronic ordering in the film is associated with a strongly inhomogeneous polaron effect. We propose to consider the interfacial tuning as a powerful mechanism to control the charge ordering in correlated electronic systems.
We study the magnetic Compton profile (MCP) of the disordered Fe$_{0.5}$Ni$_{0.5}$ and of the ordered FeNi alloys and discuss the interplay between structural disorder and electronic correlations. The Coherent Potential Approximation is employed to model the substitutional disorder within the single-site approximation, while local electronic correlations are captured with the Dynamical Mean Field Theory. Comparison with the experimental data reveals the limitation of local spin-density approximation in low momentum region, where we show that including local but dynamic correlations the experim…
We propose a dynamical mean field approach for calculating the electronic structure of strongly correlated materials from first principles. The scheme combines the GW method with dynamical mean field theory, which enables one to treat strong interaction effects. It avoids the conceptual problems inherent to conventional ``LDA+DMFT'', such as Hubbard interaction parameters and double counting terms. We apply a simplified version of the approach to the electronic structure of nickel and find encouraging results.
Quantum materials with tunable correlated and/or topological electronic states, such as the electronic Kagome lattice, provide an ideal platform to study the exotic quantum properties. However, the real-space investigations on the correlated electronic Kagome lattice have been rarely reported. Herein, we report on the electronic Kagome lattice emerging in the correlated charge-density-wave (CDW) state of 1T-TaS$_2$ at ~200 K via variable-temperature scanning tunneling microscopy (VT-STM). This emergent Kagome lattice can be considered a fractional electron-filling superstructure with reduced t…
The method of electronic structure calculations for strongly correlated disordered materials is developed employing the basic idea of coherent potential approximation (CPA). Evolution of electronic structure and spin magnetic moment value with concentration $x$ in strongly correlated Ni$_{1-x}$Zn$_x$O solid solutions is investigated in the frame of this method. The obtained values of energy gap and magnetic moment are in agreement with the available experimental data.
Motivated by the increasing number of systems featuring multiple bands at low energy, we address the Boltzmann approach to transport in a multiband weakly disordered noninteracting crystal subject to a small electric field. In general, the multiband structure leads to a considerable complication of the Boltzmann equation. Indeed, even in the presence of elastic impurity scattering, one needs to compute for each band and momentum the dressed velocities, which account for scattering events. Here we provide a semianalytical solution to the Boltzmann equation that reduces such a challenging numeri…
ComDMFT is a massively parallel computational package to study the electronic structure of correlated-electron systems (CES). Our approach is a parameter-free method based on ab initio linearized quasiparticle self-consistent GW (LQSGW) and dynamical mean field theory (DMFT). The non-local part of the electronic self-energy is treated within ab initio LQSGW and the local strong correlation is treated within DMFT. In addition to ab initio LQSGW+DMFT, charge self-consistent LDA+DMFT methodology is also implemented, enabling multiple methods in one open-source platform for the electronic structur…
We describe the correlated electronic structure of a prototype Fe-pnictide superconductor, $SmO_{1-x}F_{x}FeAs$, using LDA+DMFT. Strong, multi-orbital electronic correlations generate a low-energy pseudogap in the undistorted phase, giving a bad, incoherent metal in qualitative agreement with observations. Very good semi-quantitative agreement with the experimental spectral functions is seen, and interpreted, within a correlated, multi-orbital picture. Our results show that Fe-pnictides should be understood as low-carrier density, incoherent metals, in resemblance to the underdoped cuprate sup…
Atomic-scale precision epitaxy of perovskite oxide superlattices provides unique opportunities for controlling the correlated electronic structures, activating effective control knobs for intriguing functionalities including electromagnetic, thermoelectric, and electrocatalytic behaviors. In this study, we investigated the close interplay between the atomic and electronic structures of correlated superlattices synthesized by atomic-scale precision epitaxy. In particular, we employ superlattices composed of correlated magnetic SrRuO3 (SRO) and quantum paraelectric SrTiO3 (STO) layers. In those …
Strongly correlated electron systems require the development of new theoretical schemes in order to describe their unusual and unexpected properties. The usual perturbation schemes are inadequate and new concepts must be introduced. In our scheme of calculations, the Composite Operator Method, is possible to recover, through a self-consistent calculation, a series of fundamental symmetries by choosing a suitable Hilbert space.
We compute the electronic structure, momentum resolved spectral function and optical conductivity of the new superconductor LaO$_{1-x}$F$_x$FeAs within the combination of the Density functional theory and the Dynamical Mean Field Theory. We find that the compound in the normal state is a strongly correlated metal and the parent compound is a bad metal at the verge of the metal insulator transition. We argue that the superconductivity is not phonon mediated.
