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Many-Body Delocalization as Symmetry Breaking.

S J Garratt1, J T Chalker1

  • 1Theoretical Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.

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Summary
This summary is machine-generated.

We introduce a framework where the transition between many-body localized (MBL) and ergodic phases is driven by symmetry breaking. This symmetry breaking is observed in random Floquet spin chains, impacting their spectral properties.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Many-body localization (MBL) describes a phase of matter where quantum systems fail to thermalize.
  • Ergodic phases, in contrast, exhibit thermalization and are characterized by delocalized wavefunctions.
  • Understanding the transitions between these phases is crucial for comprehending quantum dynamics.

Purpose of the Study:

  • To present a theoretical framework for the transition between many-body localized (MBL) and ergodic phases.
  • To investigate the role of symmetry breaking in this transition.
  • To analyze the spectral properties of random Floquet spin chains.

Main Methods:

  • The study employs a transfer matrix formalism acting in the space direction to analyze the spectral form factor (SFF).
  • The SFF is calculated as a function of time for random Floquet spin chains.
  • Leading eigenvalues of the transfer matrix are used to characterize the phases.

Main Results:

  • A unique leading eigenvalue of the transfer matrix characterizes the MBL phase (symmetry-unbroken).
  • Asymptotically degenerate leading eigenvalues characterize the ergodic phase and late-time dynamics (symmetry-breaking).
  • A local order parameter for the transition is identified, with long-ranged correlations only in the ergodic phase.

Conclusions:

  • The transition between MBL and ergodic phases in random Floquet spin chains is a symmetry-breaking phenomenon.
  • The spectral form factor and its leading eigenvalues serve as indicators of the underlying symmetry.
  • The developed framework provides insights into quantum thermalization and localization transitions.