Boundary chaos

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.