Two-dimensional Anderson-Hubbard model in the DMFT + Σ approximation

The density of states, the dynamic (optical) conductivity, and the phase diagram of the paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are accounted by the DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular “bare” density of states (DOS). The DMFT effective single-impurity problem is solved by numerical renormalization group (NRG). The “correlated metal,” Mott insulator, and correlated Anderson insulator phases are identified from the evolution of the density of states, optical conductivity, and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of finite size, allowing us to construct the complete zero-temperature phase diagram of the paramagnetic Anderson-Hubbard model. The localization length in our approximation is practically independent of the strength of Hubbard correlations. But the divergence of the localization length in a finite-size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.     

Localization Criteria for Anderson Models on Locally Finite Graphs

We prove spectral and dynamical localization for Anderson models on locally finite graphs using the fractional moment method. Our theorems extend earlier results on localization for the Anderson model on ℤ ^d . We establish geometric assumptions for the underlying graph such that localization can be proven in the case of sufficiently large disorder.     

Competition of disorder and interchain hopping in a two-chain Hubbard model

We study the interplay of Anderson localization and interaction in a two chain Hubbard ladder allowing for arbitrary ratio of disorder strength to interchain coupling. We obtain three different types of spin gapped localized phases depending on the strength of disorder: a pinned 4k _F Charge Density Wave (CDW) for weak disorder, a pinned 2k _F CDW^π for intermediate disorder and two independently pinned single chain 2k _F CDW for strong disorder. Confinement of electrons can be obtained as a result of strong disorder or strong attraction. We give the full phase diagram as a function of disorder, interaction strength and interchain hopping. We also study the influence of interchain hopping on localization length and show that localization is enhanced by a small interchain hopping but suppressed by a large interchain hopping. Received 6 April 2001     

Finite-size scaling of the level compressibility at the Anderson transition

We compute the number level variance Σ ₂ and the level compressibility χ from high precision data for the Anderson model of localization and show that they can be used in order to estimate the critical properties at the metal-insulator transition by means of finite-size scaling. With N, W, and L denoting, respectively, linear system size, disorder strength, and the average number of levels in units of the mean level spacing, we find that both χ(N, W) and the integrated Σ ₂ obey finite-size scaling. The high precision data was obtained for an anisotropic three-dimensional Anderson model with disorder given by a box distribution of width W/2. We compute the critical exponent as ν≈ 1.45±0.12 and the critical disorder as W _c≈ 8.59±0.05 in agreement with previous transfer-matrix studies in the anisotropic model. Furthermore, we find χ≈ 0.28±0.06 at the metal-insulator transition in very close agreement with previous results. Received 1st November 2001 and Received in final form 8 March 2002 Published online 6 June 2002     

Anderson Localization in Dissipative Lattices

Anderson localization predicts that wave spreading in disordered lattices can come to a complete halt, providing a universal mechanism for dynamical localization. In the one-dimensional Hermitian Anderson model with uncorrelated diagonal disorder, there is a one-to-one correspondence between dynamical localization and spectral localization, that is, the exponential localization of all the Hamiltonian eigenfunctions. This correspondence can be broken when dealing with disordered dissipative lattices. When the system exchanges particles with the surrounding environment and random fluctuations of the dissipation are introduced, spectral localization is observed but without dynamical localization. Previous studies consider lattices with mixed conservative (Hamiltonian) and dissipative dynamics and are restricted to a semiclassical analysis. However, Anderson localization in purely dissipative lattices, displaying an entirely Lindbladian dynamics, remains largely unexplored. Here the purely-dissipative Anderson model in the framework of a Lindblad master equation is considered, and it is shown that, akin to the semiclassical models with conservative hopping and random dissipation, one observes dynamical delocalization in spite of strong spectral localization of the Liouvillian superoperator. This result is very distinct from delocalization observed in the Anderson model with dephasing, where dynamical delocalization arises from the delocalization of the stationary state of the Liouvillian.     

Non-Hermitian topological Anderson insulators

Non-Hermitian systems can exhibit exotic topological and localization properties.Here we elucidate the non-Hermitian effects on disordered topological systems using a nonreciprocal disordered Su-Schrieffer-Heeger model.We show that the non-Hermiticity can enhance the topological phase against disorders by increasing bulk gaps.Moreover,we uncover a topological phase which emerges under both moderate non-Hermiticity and disorders,and is characterized by localized insulating bulk states with a disorder-averaged winding number and zero-energy edge modes.Such topological phases induced by the combination of non-Hermiticity and disorders are dubbed non-Hermitian topological Anderson insulators.We reveal that the system has unique non-monotonous localization behavior and the topological transition is accompanied by an Anderson transition.These properties are general in other non-Hermitian models.     

Localization for off-diagonal disorder and for continuous Schrödinger operators

We extend the proof of localization by Delyon, Lévy, and Souillard to accommodate the Anderson model with off-diagonal disorder and the continuous Schrödinger equation with a random potential.Work supported in part by Nato under Nato Grant # 346/84Research partially supported by USNSF under grant DMS 84-16049     

Anderson Localization in the Induced Disorder System

We propose a coherently prepared three-level atomic medium that can provide a flexible disordered scheme for realizing the Anderson localization.Different disorder levels can be attained by modulating the intensity ratio between the two control beams.Due to the real-time tunability,the localization of the signal beam is observable and controllable.The influences of the induced disorder level,atomic density and the initial waist radius of the signal beam on the Anderson localization in the medium are also discussed.     

Localization in the CPA frame for alloys

To describe electron localization in substitutionally random alloysA _c B _1–c the coherent potential approximation (CPA) is incorporated into the self-consistent theory of Anderson localization in the form developed by Vollhardt and Wölfle. Modifications of the localization theory arise from the tight-binding model with bimodal diagonal disorder of arbitrary strength. The mean-free path, correlation and localization lengths, and the zero-temperature conductivity are calculated at dimensionalityd=3. The metal-insulator transition is studied numerically for a CPA-induced band structure under semielliptical model assumptions.     

Many-body effects in core-level spectroscopy of rare-earth compounds

Many-body effects in core-level photoemission and core-level photoabsorption are discussed for rare-earth systems, especially for Ce and La compounds, both in metallic and insulating forms. Emphasis is put on effects of metallic mixed valency and insulating covalency of 4f electrons on these spectra. For the insulating compound CeO₂, detailed analyses of the 3d core photoemission (3d-XPS) and the 2p core photoabsorption (L₃-XAS) are presented by using the impurity Anderson model with a filled valence band. In order to give a consistent interpretation for 3d-XPS and L₃-XAS, it is shown to be essential to take account of the Coulomb interactions U _fd (between a 4f electron and a photoexcited 5d electron in the L₃-XAS) and -U _dc (between the 5d electron and a core hole), in addition to -U _fc (between the 4f electron and the core hole). Discussions are given on the physical information derived from the analysis, on similarities and differences in spectral features between insulating and metallic systems, and also on some related topics.     

Incipient localization and tight-binding superconductivity:T c calculation

Localization effects on the superconducting transition temperatureT _c are examined in strongly disordered three-dimensional systems. A tight-binding formulation of strong-coupling superconductivity is combined, after configuration averaging, with the selfconsistent treatment of Anderson localization developed by Wollhardt and Wölfle. The Coulomb interaction becomes retarded via the joint local density of states, giving rise to an enhancement of the pseudopotential. NumericalT _c results as a function of disorder are compared with another theoretical work and experimental values for some high-T _c materials.     

Influence of local spin polarization to the Kondo effect

We use the spin non-degenerate single impurity Anderson model to investigate the influence of the local spin polarization to the Kondo effect. By using the Schrieffer-Wolff transformation, we obtain a generalized s-d exchange Hamiltonian, which describes the interaction between a polarized local spin and conduction electrons. In this case, the singlet is no longer an eigenstate as shown by variational calculations where the splitting of the local energy Δ = ɛ _d↑ − ɛ _d↓ can be arbitrarily small. The local spin polarization generates the instability of the singlet ground state of the S = 1/2 s-d exchange model.      

The Anderson transition in three-dimensional quasiperiodic lattices: finite-size scaling and critical exponent

The influence of quasiperiodicity on the metalinsulator transition (MIT) in the Anderson model of localization is investigated. The eigenstates of a 3D Amman-Kramer lattice are studied in the vertex model. The participation numbers are calculated and evaluated by means of a finitesize scaling procedure to characterize the MIT. The critical disorder W _c = 21.2 ± 0.6 and the exponent υ = 1.4 ± 0.3 are computed.     

Numerical studies on the anderson localization problem

The electron localization is studied for Anderson's tight-binding model with diagonal and off-diagonal disorder for a very large square lattice (10,000 sites) and diamond lattice (27,000 sites). The numerical investigations are based on the Lanczos recursion method. The convergence of the recursion coefficientsa _n ,b _n is discussed with regard to the electron localization.From Anderson's criterion and an exact real space renormalization method the energy of the localization edge is found as a function of the degree of disorder. Also the dependence of the spatial decay rate of localized wave functions on the energy and the degree of disorder is evaluated. Near the Anderson transition, where all states become localized, we get two critical exponentsv _E andv _W , which lead us to the tentative suggestion of multicritical scaling laws for this transition.     

Mott-Hubbard transition and Anderson localization: A generalized dynamical mean-field theory approach

The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamic conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition. The text was submitted by the authors in English.     

Energy level statistics in disordered metals with an anderson transition

We present numerical scaling results for the energy level statistics in orthogonal and symplectic tight-binding Hamiltonian random matrix ensembles defined on disordered two and three-dimensional electronic systems with and without spinorbit coupling (SOC), respectively. In the metallic phase for weak disorder the nearest level spacing distribution functionP(S), the number variance <(N)²>, and the two-point correlation functionK ₂(), are shown to be described by the Gaussian random matrix theories. In the insulating phase, for strong disorder, the correlations vanish for large scales and the ordinary Poisson statistics is asymptotically recovered, which is consistent with localization of the corrosponding eigenstates. At the Anderson metal-insulator transition we obtain new universal scale-invariant distribution functions describing the critical spectral density fluctuations.     

Random Walks and Polymers in the Presence of Quenched Disorder

After a general introduction to the field, we describe some recent results concerning disorder effects on both ‘random walk models’, where the random walk is a dynamical process generated by local transition rules, and on ‘polymer models’, where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points: thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures T _c(i,L) over the ensemble of samples (i) of size L. We describe the results of this analysis for the bidimensional wetting and for the Poland–Scheraga model of DNA denaturation.Conference Proceedings “Mathematics and Physics”, I.H.E.S., France, November 2005     

A local moment approach to the gapped Anderson model

We develop a non-perturbative local moment approach (LMA) for the gapped Anderson impurity model (GAIM), in which a locally correlated orbital is coupled to a host with a gapped density of states. Two distinct phases arise, separated by a level-crossing quantum phase transition: a screened singlet phase, adiabatically connected to the non-interacting limit and as such a generalized Fermi liquid (GFL); and an incompletely screened, doubly degenerate local moment (LM) phase. On opening a gap (δ) in the host, the transition occurs at a critical gap δ_c, the GFL [LM] phase occurring for δ<δ_c [ δ>δ_c] . In agreement with numerical renormalization group (NRG) calculations, the critical δ_c = 0 at the particle-hole symmetric point of the model, where the LM phase arises immediately on opening the gap. In the generic case by contrast δ_c > 0, and the resultant LMA phase boundary is in good quantitative agreement with NRG results. Local single-particle dynamics are considered in some detail. The major difference between the two phases resides in bound states within the gap: the GFL phase is found to be characterised by one bound state only, while the LM phase contains two such states straddling the chemical potential. Particular emphasis is naturally given to the strongly correlated, Kondo regime of the model. Here, single-particle dynamics for both phases are found to exhibit universal scaling as a function of scaled frequency ω/ω_m ⁰ for fixed gaps δ/ω_m ⁰, where ω_m ⁰ is the characteristic Kondo scale for the gapless (metallic) AIM; at particle-hole symmetry in particular, the scaling spectra are obtained in closed form. For frequencies |ω|/ω_m ⁰ ≫δ/ω_m ⁰, the scaling spectra are found generally to reduce to those of the gapless, metallic Anderson model; such that for small gaps δ/ω_m ⁰≪ 1 in particular, the Kondo resonance that is the spectral hallmark of the usual metallic Anderson model persists more or less in its entirety in the GAIM.     

Sr2FeMoO6: A Prototype to Understand a New Class of Magnetic Materials

We propose a new mechanism to explain the magnetic structure of a recently discovered magnetoresistive double perovskite oxide system, Sr₂FeMoO₆, with the help of detailed experimental and theoretical results. This model, based on a strong antiferromagnetic coupling between the local moment and the charge carriers arising from local hopping interactions, can give rise to ferromagnetic metallic as well as ferromagnetic insulating ground states. The relevance of this mechanism in understanding the magnetism in dilute magnetic semiconductors such as Ga_{1 − x} Mn _x As, is also discussed.