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Numerical Methods for Many-Body Quantum Dynamics

Citation

White, Christopher David (2019) Numerical Methods for Many-Body Quantum Dynamics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/VC0P-3K15. https://resolver.caltech.edu/CaltechTHESIS:05292019-112014488

Abstract

This thesis describes two studies of the dynamics of many-body quantum systems with extensive numerical support.

In Part I we first give a new algorithm for simulating the dynamics of one-dimensional systems that thermalize (that is, come to local thermal equilibrium). The core of this algorithm is a new truncation for matrix product operators, which reproduces local properties faithfully without reproducing non-local properties (e.g. the information required for OTOCs). To the extent that the dynamics depends only on local operators, timesteps interleaved with this truncation will reproduce that dynamics.

We then apply this to algorithm to Floquet systems: first to clean, non-integrable systems with a high-frequency drive, where we find that the system is well-described by a natural diffusive phenomenology; and then to disordered systems with low-frequency drive, which display diffusion — not subdiffusion — at appreciable disorder strengths.

In Part II, we study the utility of many-body localization as a medium for a thermodynamic engine. We first construct a small ("mesoscale") engine that gives work at high efficiency in the adiabatic limit, and show that thanks to the slow spread of information in many body localized systems, these mesoscale engines can be chained together without specially engineered insulation. Our construction takes advantage of precisely the fact that MBL systems do not thermalize. We then show that these engines still have high efficiency when run at finite speed, and we compare to competitor engines.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Numerical methods, condensed matter theory, thermalization, many body localization, quantum thermodynamics, matrix product states, dynamics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Refael, Gil
Group:Institute for Quantum Information and Matter
Thesis Committee:
  • Motrunich, Olexei I. (chair)
  • Mong, Roger S.
  • Endres, Manuel A.
  • Refael, Gil
Defense Date:16 May 2019
Funders:
Funding AgencyGrant Number
NSFDGE1144469
Gordon and Betty Moore FoundationUNSPECIFIED
NSFDMR-1410435
Packard FoundationUNSPECIFIED
NSFPHY0803371
NSFDMR-1653271
Institute for Theoretical Atomic, Molecular, and Optical Physics at Harvard UniversityUNSPECIFIED
Smithsonian Astrophysical ObservatoryUNSPECIFIED
Walter Burke FoundationUNSPECIFIED
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
W. M. Keck FoundationUNSPECIFIED
NSFDGE1745301
Record Number:CaltechTHESIS:05292019-112014488
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:05292019-112014488
DOI:10.7907/VC0P-3K15
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/physrevb.97.035127DOIArticle adapted for Ch. II.
http://arxiv.org/abs/1902.01859v1arXivArticle adapted for Ch. III.
https://doi.org/10.1103/physrevb.97.035127DOIArticle adapted for Part II.
ORCID:
AuthorORCID
White, Christopher David0000-0002-8372-2492
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11558
Collection:CaltechTHESIS
Deposited By: Christopher White
Deposited On:10 Jun 2019 22:30
Last Modified:02 Jun 2020 21:41

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