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Surviving Quantum Chaos: Weak Thermalization, Prethermalization and Quantum Many-Body Scar States

Citation

Lin, Cheng-Ju (2019) Surviving Quantum Chaos: Weak Thermalization, Prethermalization and Quantum Many-Body Scar States. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/DKYP-PH92. https://resolver.caltech.edu/CaltechTHESIS:05232019-192004916

Abstract

Quantum chaos and the eigenstate thermalization hypothesis are based on the assumption of the validity of random matrix theory description on the spectrum and eigenstates. They provide the foundation and descriptions for the typical dynamics and thermalization in generic closed quantum systems. In this thesis, we investigate situations where the systems show atypical dynamics or anomalous thermalization, conflicting with the usual expectations from quantum chaos and eigenstate thermalization hypothesis. We first examine weak thermalization in a nonintegrable spin chain. The system shows long-lived strong oscillations and relaxes to the thermal equilibrium weakly. We identify the dynamics describable by quasiparticles and recognize the oscillation frequency to be the quasiparticle mass gap. We also estimate the damping time for the oscillations. Next, we study prethermalization, a phenomenon where a system relaxes to an intermediate almost-equilibrium stage before reaching the true thermal equilibrium. We study a nonintegrable spin chain in the strong coupling limit, where an almost-conserved quantity emerges and gives rise to the prethermalization. We also study a newly proposed diagnostic for quantum chaos: out-of-time-ordered correlators. Contrasting to the chaotic systems, we inspect their behaviors in various noninteracting integrable models. Finally, we dig into the quantum many-body scar states in the PXP model which describes a Rydberg atom chain. These special states do not satisfy the random matrix theory description nor the eigenstate thermalization hypothesis, therefore defying quantum chaos.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Quantum chaos; weak thermalization; prethermalization; out-of-time-ordered correlators; Ising model; hard-core boson model; Luttinger liquid model; quantum many-body scar states; Schrieffer-Wolff transformation; slowest operator algorithm; PXP model; Rydberg atom chain
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Awards:Robert F. Christy Prize for an Outstanding Doctoral Thesis in Theoretical Physics, 2019.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Motrunich, Olexei I.
Thesis Committee:
  • Alicea, Jason F. (chair)
  • Motrunich, Olexei I.
  • Chen, Xie
  • Hsieh, David
Defense Date:22 May 2019
Non-Caltech Author Email:jacob0425 (AT) gmail.com
Record Number:CaltechTHESIS:05232019-192004916
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:05232019-192004916
DOI:10.7907/DKYP-PH92
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevA.95.023621DOIArticle adapted for Ch. 2.
https://doi.org/10.1103/PhysRevB.96.214301DOIArticle adapted for Ch. 3.
https://doi.org/10.1103/PhysRevB.97.144304DOIArticle adapted for Ch. 4.
https://doi.org/10.1103/PhysRevB.98.134305DOIArticle adapted for Ch. 4.
https://doi.org/10.1103/PhysRevLett.122.173401DOIArticle adapted for Ch. 5.
ORCID:
AuthorORCID
Lin, Cheng-Ju0000-0001-7898-0211
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11538
Collection:CaltechTHESIS
Deposited By: Cheng Ju Lin
Deposited On:01 Jun 2019 00:45
Last Modified:04 Oct 2019 00:25

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