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Information Scrambling in Quantum Many-Body Systems

Citation

Zhang, Yongliang (2020) Information Scrambling in Quantum Many-Body Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/GDZ1-0G66. https://resolver.caltech.edu/CaltechTHESIS:02262020-182938837

Abstract

A closed quantum system never forgets its initial state, but the encoded information can get scrambled and become inaccessible without measuring a large fraction of all the system degrees of freedom. This scrambling can be diagnosed by studying the spatial spreading of initially local operators under the Heisenberg time evolution, and the decay of the out-of-time-ordered correlators (OTOC). What insights can OTOCs provide to understand the dynamics of quantum many-body systems? What are the characteristic behaviors of OTOCs during the time evolution? How is information scrambling affected by the dissipation in open quantum many-body systems?

We first study slow scrambling in many-body localized systems via calculating various correlators, two-point retarded correlators and OTOCs. Comparing with retarded correlators, OTOCs provide more information about the dynamics. We find that disorder slows and partially halts the onset of information scrambling. Instead of ballistic spreading, propagation of information forms a logarithmic light cone.

Next, we study the finite-size scaling of OTOCs at late times in generic thermalizing quantum many-body systems. When energy is conserved, the late-time saturation value of the OTOC of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation.

We also study information scrambling in open quantum many-body systems. We define a dissipative version of OTOC and study its behaviors in a prototypical chaotic quantum chain with dissipation. We find that dissipation leads to not only the overall decay of the scrambled information due to leaking, but also structural changes so that the information light cone can only reach a finite distance even when the effect of overall decay is removed.

Finally, we construct a family of local Hamiltonians for understanding the asymmetric information scrambling. Our models live on a one-dimensional lattice and exhibit asymmetric butterfly light cone between the left and right spatial directions.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Information Scrambling, out-of-time-ordered correlator, butterfly velocity
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Minor Option:Computer Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Chen, Xie
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Thesis Committee:
  • Brandao, Fernando (chair)
  • Alicea, Jason F.
  • Chen, Xie
  • Endres, Manuel A.
Defense Date:20 February 2020
Non-Caltech Author Email:ylzhang.cit (AT) gmail.com
Record Number:CaltechTHESIS:02262020-182938837
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:02262020-182938837
DOI:10.7907/GDZ1-0G66
Related URLs:
URLURL TypeDescription
https://doi.org/10.1002/andp.201600318DOIArticle adapted for Chapter 2.
https://doi.org/10.1103/PhysRevLett.123.010601DOIArticle adapted for Chapter 3.
https://doi.org/10.1103/PhysRevB.99.014303DOIArticle adapted for Chapter 4.
https://arxiv.org/abs/1909.03988arXivArticle adapted for Chapter 5.
ORCID:
AuthorORCID
Zhang, Yongliang0000-0002-8246-3759
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13644
Collection:CaltechTHESIS
Deposited By: Yongliang Zhang
Deposited On:28 Feb 2020 22:09
Last Modified:18 Dec 2020 00:23

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