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The characterizing feature of a many-body localized phase is the existence of an extensive set of quasi-local conserved quantities with an exponentially localized support. This structure endows the system with the signature logarithmic in…
We establish non-perturbative Anderson localization for a wide class of 1D quasiperiodic operators with unbounded monotone potentials, extending the classical results on Maryland model and perturbative results for analytic potentials by…
We present a novel approximation scheme for the treatment of strongly correlated electrons in arbitrary crystal lattices. The approach extends the well-known dynamical mean field theory to include nonlocal two-site correlations of arbitrary…
We generate translationally invariant systems exhibiting many-body localization from All-Bands- Flat single particle lattice Hamiltonians dressed with suitable short-range many-body interactions. This phenomenon - dubbed Many-Body Flatband…
Recently, it has been suggested that the Many-Body Localized phase can be characterized by local integrals of motion. Here we introduce a Hilbert space preserving renormalization scheme that iteratively finds such integrals of motion…
Through a combination of rigorous analytical derivations and extensive numerical simulations, this work reports an exotic multifractal behavior, dubbed "logarithmic multifractality", in effectively infinite-dimensional systems undergoing…
Ballooning instabilities are investigated in three-dimensional magnetic toroidal plasma confinement systems with low global magnetic shear. The lack of any continuous symmetry in the plasma equilibrium can lead to these modes being…
In this paper, we prove the large deviation estimates and Anderson localization for CMV matrices on $\ell^2(\mathbb{Z}_+)$ with Verblunsky coefficients defined dynamically by the hyperbolic toral automorphism. Part of positivity results on…
We use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional, continuum, Anderson-type models with singular distributions; in particular the case of a Bernoulli distribution is covered. The…
A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated…
We give a widely self-contained introduction to the mathematical theory of the Anderson model. After defining the Anderson model and determining its almost sure spectrum, we prove localization properties of the model. Here we discuss…
We consider a weakly interacting quantum spin chain with random local interactions. We prove that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of…
We report on phenomenon of Anderson-type localization of walking solitons in optical lattices with random frequency modulation, manifested as dramatic enhancement of soliton trapping probability on lattice inhomogeneities with growth of the…
We construct the generic phase diagrams encoding the topologically distinct localized and delocalized phases of noninteracting fermionic quasiparticles for any symmetry class from the tenfold way in one, two, and three dimensions. To this…
We prove exponential spectral localization in a two-particle lattice Anderson model, with a short-range interaction and external random i.i.d. potential, at sufficiently low energies. The proof is based on the multi-particle multi-scale…
We develop a systematic typical medium dynamical cluster approximation that provides a proper description of the Anderson localization transition in three dimensions (3D). Our method successfully captures the localization phenomenon both in…
These lectures present some basic ideas and techniques in the spectral analysis of lattice Schrodinger operators with disordered potentials. In contrast to the classical Anderson tight binding model, the randomness is also allowed to…
We construct a quasiperiodic lattice model in curved spacetime to explore the crossover concerning both condensed matter and curved spacetime physics. We study the related Anderson localization and find that the model has a clear boundary…
We predict the quantum correlations between non-interacting particles evolving simultaneously in a disordered medium. While the particle density follows the single-particle dynamics and exhibits Anderson localization, the two-particle…
Based on the statistical dynamical mean field theory, we investigate, in a generic model for a strongly coupled disordered electron-phonon system, the competition between polaron formation and Anderson localization. The statistical…