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Relaxation Exponents of OTOCs and Overlap with Local Hamiltonians.
Vinitha Balachandran1, Dario Poletti1,2,3,4,5
1Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore.
Quantum information scrambling, measured by OTOC, is influenced by local conserved quantities. Higher exponents of the Hamiltonian lead to faster, albeit algebraic, relaxation dynamics in quantum systems.
Area of Science:
- Quantum Information Science
- Condensed Matter Physics
- Quantum Dynamics
Background:
- Out-of-Time-Order Correlators (OTOC) are key to understanding information scrambling in quantum systems.
- Local conserved quantities significantly impact OTOC relaxation in non-integrable systems, often causing slow scrambling.
Purpose of the Study:
- Investigate the role of higher powers of the Hamiltonian in OTOC dynamics.
- Determine how observable-Hamiltonian overlap at elevated exponents affects relaxation rates.
Main Methods:
- Analytical derivation of OTOC relaxation behavior for observables with overlap at higher Hamiltonian powers.
- Numerical simulations to validate analytical predictions.
Main Results:
- Higher exponents of the Hamiltonian lead to faster, algebraic relaxation of OTOC.
- These exponents can increase indefinitely, suggesting tunable relaxation timescales.
Conclusions:
- The study reveals a mechanism for faster information scrambling in quantum systems by considering higher Hamiltonian powers.
- Findings provide new insights into controlling quantum dynamics and information scrambling.
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