Many-body localization in periodically driven systems

TL;DR

This paper investigates how many-body localization persists under periodic driving in disordered one-dimensional systems, identifying distinct localized and delocalized phases with different entanglement properties and proposing an effective model for the MBL phase.

Contribution

It demonstrates the existence of a many-body localized phase under periodic driving and introduces an effective model based on local integrals of motion to explain its properties.

Findings

MBL phase exhibits area-law entanglement and violates ETH.

Delocalized phase shows volume-law entanglement and obeys ETH.

Numerical data suggests a direct transition between phases.

Abstract

We consider disordered many-body systems with periodic time-dependent Hamiltonians in one spatial dimension. By studying the properties of the Floquet eigenstates, we 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, in which eigenstates have volume-law entanglement and obey the ETH. MBL phase exhibits logarithmic in time growth of entanglement entropy for initial product states, which distinguishes it from the delocalized phase. We propose an effective model of the MBL phase in terms of an extensive number of emergent local integrals of motion (LIOM), which naturally explains the spectral and dynamical properties of this phase. Numerical data, obtained by exact diagonalization and time-evolving block decimation methods, suggests a direct transition between the two phases. Our results show that many-body localization is not destroyed by sufficiently weak periodic driving.