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Relaxation exponents of OTOCs and overlap with local Hamiltonians (2211.09965v2)
Published 18 Nov 2022 in cond-mat.stat-mech and quant-ph
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.