From ETH to algebraic relaxation of OTOCs in systems with conserved quantities

Abstract

The relaxation of out-of-time-ordered correlators (OTOCs) has been studied as a mean to characterize the scrambling properties of a quantum system. We show that the presence of local conserved quantities typically results in, at the fastest, an algebraic relaxation of the OTOC provided (i) the dynamics is local and (ii) the system follows the eigenstate thermalization hypothesis. Our result relies on the algebraic scaling of the infinite-time value of OTOCs with system size, which is typical in thermalizing systems with local conserved quantities, and on the existence of finite speed of propagation of correlations for finite-range-interaction systems. We show that time-independence of the Hamiltonian is not necessary as the above conditions (i) and (ii) can occur in time-dependent systems, both periodic or aperiodic. We also remark that our result can be extended to systems with power-law interactions.

14 pages, 7 figures

References in corpus (14)

• The density-matrix renormalization group in the age of matrix product states
• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• Real time evolution using the density matrix renormalization group
• Black holes as mirrors: quantum information in random subsystems
• The Magnus expansion and some of its applications
• Breakdown of thermalization in finite one-dimensional systems
• Recent progress in many-body localization
• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• Nearly-linear light cones in long-range interacting quantum systems
• Sufficient conditions for the convergence of the Magnus expansion
• Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator
• Quantum Chaos and the Correspondence Principle

Cited by in corpus (15)

• Scrambling is Necessary but Not Sufficient for Chaos
• Chaos and Thermalization in the Spin-Boson Dicke Model
• Hydrodynamics and the eigenstate thermalization hypothesis
• BROTOCs and Quantum Information Scrambling at Finite Temperature
• Scaling laws of the out-of-time-order correlators at the transition to the spontaneous $\mathcal{P}\mathcal{T}$-symmetry breaking in a Floquet system
• Unraveling the emergence of quantum state designs in systems with symmetry
• Slow relaxation of out-of-time-ordered correlators in interacting integrable and nonintegrable spin-1/2 XYZ chains
• Quantum Lyapunov exponent in dissipative systems
• Quantum algorithm for evaluating operator size with Bell measurements
• Temporal fluctuations of correlators in integrable and chaotic quantum systems
• Out-of-Time Ordered Correlators in Kicked Coupled Tops: Information Scrambling in Mixed Phase Space and the Role of Conserved Quantities
• Relaxation exponents of OTOCs and overlap with local Hamiltonians
• Key Observable for Linear Thermalization
• Learning out-of-time-ordered correlators with classical kernel methods
• Symmetry resolved out-of-time-order correlators of Heisenberg spin chains using projected matrix product operators