François Huveneers

TL;DR: In this article, the authors consider disordered many-body systems with periodic time-dependent Hamiltonians in one spatial dimension and identify two distinct phases: (i) a many body localized (MBL) phase, in which almost all eigenstates have area-law entanglement entropy, and the eigenstate thermalization hypothesis (ETH) is violated, and (ii) a delocalized phase, where eigen states have volume-law entropy and obey the ETH.

TL;DR: It is shown that, for systems with local interactions, the energy absorption rate decays exponentially as a function of driving frequency in any number of spatial dimensions, implying that topological many-body states in periodically driven systems, although generally metastable, can have very long lifetimes.

TL;DR: In this article, the stability of a many-body localized material in contact with an ergodic grain was investigated and it was shown that the ergodics are always present as Griffiths regions where disorder is anomalously small, and hence, the authors conclude that the localized phase in such materials is unstable, strictly speaking.

TL;DR: In this paper, it was shown that a quantum many-body system with a high-frequency periodic driving has a quasiconserved extensive quantity, which plays the role of an effective static Hamiltonian, and that the energy absorption rate is exponentially small in the driving frequency.

TL;DR: In this paper, the authors considered the Fermi-Hubbard model with periodic driving at high frequency and showed that up to a quasi-exponential time, the system barely absorbs energy.