Relaxation exponents of OTOCs and overlap with local Hamiltonians

TL;DR

This paper investigates how the relaxation dynamics of out-of-time-ordered correlators (OTOCs) are influenced by their overlap with local conserved quantities and higher powers of the Hamiltonian, revealing that higher exponents lead to faster algebraic relaxation.

Contribution

It introduces the concept that overlaps with higher powers of the Hamiltonian accelerate OTOC relaxation, extending understanding beyond linear overlaps.

Findings

Higher exponents correspond to faster relaxation.

Relaxation remains algebraic even with higher exponents.

Numerical results support analytical predictions.

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.