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Scrambling Dynamics across a Thermalization-Localization Quantum Phase Transition.

Subhayan Sahu1, Shenglong Xu1, Brian Swingle2

  • 1Condensed Matter Theory Center and Department of Physics, University of Maryland, College Park, Maryland 20742, USA.

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|November 9, 2019
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Summary
This summary is machine-generated.

We studied quantum information scrambling in disordered spin chains. We found a transition from ballistic to subballistic operator growth, occurring before the localization transition.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Quantum information theory

Background:

  • Quantum information scrambling describes how quantum information spreads in a quantum system.
  • Disordered quantum systems can exhibit transitions between thermalization and localization.
  • Understanding these transitions is key to quantum computing and materials science.

Purpose of the Study:

  • To investigate quantum information scrambling in disordered spin chains.
  • To map the transition from thermalization to localization using operator growth dynamics.
  • To characterize the nature of operator spreading across this quantum phase transition.

Main Methods:

  • Utilizing matrix product operator (MPO) dynamics to simulate large disordered spin chains.
  • Scanning across the thermalization-localization quantum phase transition.
  • Analyzing the growth of Heisenberg operators to probe scrambling dynamics.
  • Employing finite-size scaling of entanglement entropy to determine localization transitions.

Main Results:

  • Observed ballistic operator growth in the weak disorder regime.
  • Identified a sharp transition to subballistic operator spreading at a critical disorder strength.
  • Found this transition occurs significantly below the many-body localization transition.
  • Determined that the transition to logarithmic operator spreading at the localization transition is not resolved in current numerical simulations.

Conclusions:

  • The transition to subballistic operator spreading is a distinct phenomenon preceding full localization.
  • Rare regions likely play a crucial role in the observed operator spreading dynamics.
  • The study provides insights into the universal behavior of growing operators near quantum phase transitions.