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Title:Delocalization phenomena in strongly disordered systems
Author(s):Mondragon Shem, Ian
Director of Research:Hughes, Taylor L
Doctoral Committee Chair(s):Ryu, Shinsei
Doctoral Committee Member(s):Mason, Nadya; Dahmen, Karin
Department / Program:Physics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Anderson localization
Disordered systems
Topological phases
Quantum phase transitions
Many-body localization
Abstract:In this dissertation, we study delocalization mechanisms in strongly disordered systems. We focus on one-dimensional systems where the localizing effects of disorder are strongest. Our explorations of delocalization mechanisms will reveal new insights into the nature of Anderson transitions in the context of the entanglement, topology and interactions. We begin by proposing momentum entanglement as an efficient tool for detecting delocalized states in a broad class of disordered systems that undergo metal-insulator transitions. We find that the signatures of delocalized states in the momentum entanglement are remarkably clear. We explain this structure in the momentum entanglement by elucidating the underlying mechanism for delocalization in these disordered models. We will afterwards discuss a different type of delocalized state that arises at disorder-induced topological phase transitions. Anderson transitions in this case occur between insulating phases, with the emergence of critical states at the transition point. Through a mapping to a disordered spin chain, we provide a real-space description of the topology of the ground state and the delocalized state that emerges at the critical point. In this case, the mechanism that leads to delocalization reveals an unconventional type of disorder-induced topological phase transition that is fundamentally different, for example, from quantum Hall transitions. Finally, we examine delocalization processes in strongly interacting many-body localized phases. We find that strong interactions and the presence of symmetry constraints lead to an important spectral asymmetry in the localization transition. This asymmetry arises from the different dynamical properties of short-ranged correlated states that form due to having strong interactions. We explain how this asymmetry presents advantages in the numerical as well as experimental study of many-body localization transitions.
Issue Date:2016-08-01
Rights Information:Copyright 2016 Ian Mondragon Shem
Date Available in IDEALS:2017-03-01
Date Deposited:2016-12

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