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We studied quantum scrambling in many-body systems using a novel quantum circuit model. Our findings reveal how boundary impurities influence correlations, showing exponential suppression or periodic revivals based on impurity type.

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Area of Science:

  • Quantum physics
  • Many-body systems
  • Quantum information

Background:

  • Quantum scrambling describes how local quantum information spreads in many-body systems.
  • This spreading typically leads to exponential suppression of correlations with increasing system size.
  • Understanding the mechanisms of scrambling is crucial for quantum computing and condensed matter physics.

Purpose of the Study:

  • To investigate the mechanism of quantum scrambling in a simplified model.
  • To explore the role of boundary impurities in controlling quantum correlations.
  • To develop a method for studying large system sizes beyond exact diagonalization.

Main Methods:

  • Development of a perturbed free quantum circuit model with boundary impurities.
  • Mapping dynamical correlation functions to a 2D lattice partition function with complex weights.
  • Evaluation of the partition function using transfer matrices for numerical analysis.
  • Combining analytical arguments with numerical simulations.

Main Results:

  • Demonstrated that boundary impurities can induce ergodicity and control scrambling.
  • Showed that correlations are exponentially suppressed with system size for specific unitary impurities.
  • Observed persistent revivals of correlations for generic impurities or operator locations.

Conclusions:

  • The study provides a mechanism for demonstrating quantum scrambling via boundary perturbations.
  • The findings highlight the tunability of quantum correlations through impurity engineering.
  • The transfer matrix method enables the study of large-scale quantum systems, offering insights into quantum dynamics.