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Critically Slow Operator Dynamics in Constrained Many-Body Systems.

Johannes Feldmeier1, Michael Knap1

  • 1Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany and Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, D-80799 München, Germany.

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|December 22, 2021
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Summary
This summary is machine-generated.

In constrained quantum systems, conservation laws alter universal operator spreading. Researchers found a critical point in fracton chains exhibiting sub-ballistic growth, revealing a novel localization transition.

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Area of Science:

  • Quantum dynamics
  • Many-body physics
  • Condensed matter theory

Background:

  • Far-from-equilibrium dynamics in quantum systems often follow universal principles.
  • Ballistic spreading of local operators is a key characteristic of generic systems.

Purpose of the Study:

  • To investigate how conservation laws modify universal dynamics in constrained many-body systems.
  • To study operator growth in a dipole-conserving fracton chain using out-of-time-order correlations (OTOCs).

Main Methods:

  • Analysis of operator growth via OTOCs in a dipole-conserving fracton chain.
  • Identification of a critical point separating different dynamical phases.
  • Numerical simulations using classically simulable automaton circuits.

Main Results:

  • A critical point was identified where the out-of-time-order correlations (OTOCs) front moves sub-ballistically.
  • This critical point signifies a transition between a ballistic and a dynamically frozen phase.
  • The transition is linked to an underlying localization transition.

Conclusions:

  • Conservation laws can drastically alter universal quantum dynamics in constrained systems.
  • An effective description of the operator front as a biased random walk with long waiting times was derived.
  • Numerical evidence supports the theoretical findings in automaton circuits.