Local integrals of motion and the logarithmic lightcone in many-body localized systems

Abstract

We propose to define full many-body localization in terms of the recently introduced integrals of motion[Chandran et al., arXiv:1407.8480], which characterize the time-averaged response of the system to a local perturbation. The quasi-locality of such integrals of motion implies an effective lightcone that grows logarithmically in time. This subsequently implies that (i) the average entanglement entropy can grow at most logarithmically in time for a global quench from a product state, and (ii) with high probability, the time evolution of a local operator for a time interval $|t|$ can be classically simulated with a resource that scales polynomially in $|t|$.

10+0.5 pages, 2 figures, minor changes

Cited by in corpus (5)

• Integrals of motion in the Many-Body localized phase
• Slow scrambling in disordered quantum systems
• Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
• Measuring out quasi-local integrals of motion from entanglement
• Entanglement Dynamics From Random Product States: Deviation From Maximal Entanglement