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  • 1.
    Kjäll, Jonas A.
    Stockholm University, Faculty of Science, Department of Physics.
    Many-body localization and level repulsion2018In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 97, no 3, article id 035163Article in journal (Refereed)
    Abstract [en]

    Insertion of disorder in thermal interacting quantum systems decreases the amount of level repulsion and can lead to many-body localization. In this paper we use the many-body picture to perturbatively study the effect of level repulsion in the localized phase. We find that most eigenstates can be described accurately in an approximate way, including many with rare resonances. A classification of the rare resonances shows that most types are exponentially rare and requires exponential fine tuning in an approximate description. The classification confirms that no rare thermal eigenstates exist in a fully localized phase and we argue that all types of resonances need to become common if a continuous transition into a thermal phase should occur.

  • 2.
    Kjäll, Jonas
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Ardonne, Eddy
    Stockholm University, Faculty of Science, Department of Physics.
    Dwivedi, V.
    Hermanns, M.
    Hansson, Thors Hans
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Matrix product state representation of quasielectron wave functions2018In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, article id 053101Article in journal (Refereed)
    Abstract [en]

    Matrix product state techniques provide a very efficient way to numerically evaluate certain classes of quantum Hall wave functions that can be written as correlators in two-dimensional conformal field theories. Important examples are the Laughlin and Moore-Read ground states and their quasihole excitations. In this paper, we extend the matrix product state techniques to evaluate quasielectron wave functions, a more complex task because the corresponding conformal field theory operator is not local. We use our method to obtain density profiles for states with multiple quasielectrons and quasiholes, and to calculate the (mutual) statistical phases of the excitations with high precision. The wave functions we study are subject to a known difficulty: the position of a quasielectron depends on the presence of other quasiparticles, even when their separation is large compared to the magnetic length. Quasielectron wave functions constructed using the composite fermion picture, which are topologically equivalent to the quasielectrons we study, have the same problem. This flaw is serious in that it gives wrong results for the statistical phases obtained by braiding distant quasiparticles. We analyze this problem in detail and show that it originates from an incomplete screening of the topological charges, which invalidates the plasma analogy. We demonstrate that this can be remedied in the case when the separation between the quasiparticles is large, which allows us to obtain the correct statistical phases. Finally, we propose that a modification of the Laughlin state, that allows for local quasielectron operators, should have good topological properties for arbitrary configurations of excitations.

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