Delocalization phenomena in strongly disordered systems

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2017

Author dc:creator

• Mondragon Shem, Ian

Contributors dc:contributor

• Hughes, Taylor L.
• Ryu, Shinsei
• Mason, Nadya
• Dahmen, Karin

• Anderson localization
• Disordered systems
• Entanglement
• Topological phases
• Quantum phase transitions
• Many-body localization

Statement dc:rights

• Copyright 2016 Ian Mondragon Shem

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/95432