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      Extended nonergodic states in disordered many-body quantum systems : Extended nonergodic states in disordered many-body quantum systems

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      Annalen der Physik
      Wiley-Blackwell

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          Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states

          We consider low-temperature behavior of weakly interacting electrons in disordered conductors in the regime when all single-particle eigenstates are localized by the quenched disorder. We prove that in the absence of coupling of the electrons to any external bath dc electrical conductivity exactly vanishes as long as the temperatute \(T\) does not exceed some finite value \(T_c\). At the same time, it can be also proven that at high enough \(T\) the conductivity is finite. These two statements imply that the system undergoes a finite temperature Metal-to-Insulator transition, which can be viewed as Anderson-like localization of many-body wave functions in the Fock space. Metallic and insulating states are not different from each other by any spatial or discrete symmetries. We formulate the effective Hamiltonian description of the system at low energies (of the order of the level spacing in the single-particle localization volume). In the metallic phase quantum Boltzmann equation is valid, allowing to find the kinetic coefficients. In the insulating phase, \(T
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            Anderson localization of a non-interacting Bose-Einstein condensate

            One of the most intriguing phenomena in physics is the localization of waves in disordered media. This phenomenon was originally predicted by Anderson, fifty years ago, in the context of transport of electrons in crystals. Anderson localization is actually a much more general phenomenon, and it has been observed in a large variety of systems, including light waves. However, it has never been observed directly for matter waves. Ultracold atoms open a new scenario for the study of disorder-induced localization, due to high degree of control of most of the system parameters, including interaction. Here we employ for the first time a noninteracting Bose-Einstein condensate to study Anderson localization. The experiment is performed with a onedimensional quasi-periodic lattice, a system which features a crossover between extended and exponentially localized states as in the case of purely random disorder in higher dimensions. Localization is clearly demonstrated by investigating transport properties, spatial and momentum distributions. We characterize the crossover, finding that the critical disorder strength scales with the tunnelling energy of the atoms in the lattice. Since the interaction in the condensate can be controlled at will, this system might be employed to solve open questions on the interplay of disorder and interaction and to explore exotic quantum phases.
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              Observation of many-body localization of interacting fermions in a quasi-random optical lattice

              We experimentally observe many-body localization of interacting fermions in a one-dimensional quasi-random optical lattice. We identify the many-body localization transition through the relaxation dynamics of an initially-prepared charge density wave. For sufficiently weak disorder the time evolution appears ergodic and thermalizing, erasing all remnants of the initial order. In contrast, above a critical disorder strength a significant portion of the initial ordering persists, thereby serving as an effective order parameter for localization. The stationary density wave order and the critical disorder value show a distinctive dependence on the interaction strength, in agreement with numerical simulations. We connect this dependence to the ubiquitous logarithmic growth of entanglement entropy characterizing the generic many-body localized phase.
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                Author and article information

                Journal
                Annalen der Physik
                ANNALEN DER PHYSIK
                Wiley-Blackwell
                00033804
                July 2017
                July 2017
                : 529
                : 7
                : 1600284
                Article
                10.1002/andp.201600284
                8cda53fe-49bb-4bd0-8251-101492c6d398
                © 2017

                http://doi.wiley.com/10.1002/tdm_license_1.1

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