University of Illinois Urbana-Champaign

Delocalization phenomena in strongly disordered systems

Mondragon Shem, Ian

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MONDRAGONSHEM-DISSERTATION-2016.pdf

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https://hdl.handle.net/2142/95432

Description

Title
Delocalization phenomena in strongly disordered systems
Author(s)
Mondragon Shem, Ian
Issue Date
2016-08-01
Director of Research (if dissertation) or Advisor (if thesis)
Hughes, Taylor L.
Doctoral Committee Chair(s)
Ryu, Shinsei
Committee Member(s)
  • Mason, Nadya
  • Dahmen, Karin
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2017-03-01T15:51:13Z
Keyword(s)
  • Anderson localization
  • Disordered systems
  • Entanglement
  • 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.
Graduation Semester
2016-12
Type of Resource
text
Permalink
http://hdl.handle.net/2142/95432
Copyright and License Information
Copyright 2016 Ian Mondragon Shem

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