Related papers: Integrals of motion for one-dimensional Anderson l…
The interplay among topology, disorder, and non-Hermiticity can induce some exotic topological and localization phenomena. Here we investigate this interplay in a two-dimensional non-Hermitian disordered Chern-insulator model with two…
Dimension 2 is expected to be the lower critical dimension for Anderson localization in a time reversal-invariant disordered quantum system. Using an atomic quasiperiodic kicked rotor -- equivalent to a two-dimensional Anderson-like model…
Excitonic transport in static disordered one dimensional systems is studied in the presence of thermal fluctuations that are described by the Haken-Strobl-Reineker model. For short times, non-diffusive behavior is observed that can be…
We consider interacting electrons in a one dimensional lattice with an incommensurate Aubry-Andre' potential in the regime when the single-particle eigenstates are localized. We rigorously establish persistence of ground state localization…
Topic of the thesis is a theoretical description of the ultracold atomic gases in one- and two-dimensional optical lattices in the presence of the disorder leading to the Anderson localization. The disorder is created by interaction of the…
Certain disorder-free Hamiltonians can be non-ergodic due to a \emph{strong fragmentation} of the Hilbert space into disconnected sectors. Here, we characterize such systems by introducing the notion of `statistically localized integrals of…
We explore single-particle Anderson localization due to nonrandom quasiperiodic potentials in two and three dimensions. We introduce a class of self-dual models that generalize the one-dimensional Aubry-Andr\'e model to higher dimensions.…
Localization due to disorder has been one of the most intriguing theoretical concepts evolved in condensed matter. Here, we expand the theory of localization by considering two types of disorder at the same time, namely the original…
We uncover a systematic structure in the single particle phase-diagram of the quasiperiodic Aubry-Andr\'e-Harper(AAH) model with power-law hoppings ($\sim \frac{1}{r^\sigma}$) when the quasiperiodicity parameter is chosen to be a member of…
Previous studies have established that quasiperiodic lattice models with unbounded potentials can exhibit localized and multifractal states, yet preclude the existence of extended states. In this work, we introduce a quasiperiodic system…
We consider isolated quantum systems with all of their many-body eigenstates localized. We define a sense in which such systems are integrable, and discuss a method for finding their localized conserved quantum numbers ("constants of…
In the one-dimensional Anderson model the eigenstates are localized for arbitrarily small amounts of disorder. In contrast, the Harper model with its quasiperiodic potential shows a transition from extended to localized states. The…
Quasiperiodic systems are neither randomly disordered nor translationally invariant in the absence of periodic length scales. Based on their incommensurate order, novel physical properties such as critical states and self-similar…
The phenomenon of localization is usually accompanied with the presence of quenched disorder. To what extent disorder is necessary for localization is a well-known open problem. In this paper, we prove the instability of localization in…
A Dyson hierarchical model for Anderson localization, containing non-random hierarchical hoppings and random on-site energies, has been studied in the mathematical literature since its introduction by Bovier [J. Stat. Phys. 59, 745 (1990)],…
We consider the dynamics of an electron in an infinite disordered metallic wire. We derive exact expressions for the probability of diffusive return to the starting point in a given time. The result is valid for wires with or without…
We study localization properties of continuously monitored dynamics and associated measurement-induced phase transitions in disordered quantum many-body systems on the basis of the quantum trajectory approach. By calculating the fidelity…
Mobility edge (ME), a critical energy separating localized and extended states in spectrum, is a central concept in understanding the localization physics. However, there are few models with exact MEs. In the paper, we generalize the…
We study Anderson localization of single particles in continuous, correlated, one-dimensional disordered potentials. We show that tailored correlations can completely change the energy-dependence of the localization length. By considering…
We numerically investigate the momentum-space entanglement entropy and entanglement spectrum of the random-dimer model and its generalizations, which circumvent Anderson localization, after a quench in the Hamiltonian parameters. The type…