Relaxation exponents of OTOCs and overlap with local Hamiltonians
arXiv:2211.09965 · doi:10.3390/e25010059
Abstract
OTOC has been used to characterize the information scrambling in quantum systems. Recent studies showed that local conserved quantities play a crucial role in governing the relaxation dynamics of OTOC in non-integrable systems. In particular, slow scrambling of OTOC is seen for observables that has an overlap with local conserved quantities. However, an observable may not overlap with the Hamiltonian, but with the Hamiltonian elevated to an exponent larger than one. Here, we show that higher exponents correspond to faster relaxation, although still algebraic, and with exponents that can increase indefinitely. Our analytical results are supported by numerical experiments.
8 pages, 3 figures. arXiv admin note: text overlap with arXiv:2106.00234
References in corpus (8)
- Localization of interacting fermions at high temperature
- Black holes as mirrors: quantum information in random subsystems
- Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
- Information Scrambling in Computationally Complex Quantum Circuits
- Probing quantum information propagation with out-of-time-ordered correlators
- Quantum Chaos and the Correspondence Principle
- Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator
- From ETH to algebraic relaxation of OTOCs in systems with conserved quantities