Abstract
In this work we investigate the stability of an algebraically localized phase subject to periodic driving. First, we focus on a non-interacting model exhibiting algebraically localized single-particle modes. For this model we find numerically that the algebraically localized phase is stable under driving, meaning that the system remains localized at arbitrary frequencies. We support this result with analytical considerations using simple renormalization group arguments. Second, we inspect the case in which short-range interactions are added. By studying both, the eigenstates properties of the Floquet Hamiltonian and the out-of-equilibrium dynamics in the interacting model, we provide evidence that ergodicity is restored at any driving frequencies. In particular, we observe that for the accessible system sizes localization sets in at driving frequency that are comparable with the many-body bandwidth and thus it might be only transient, suggesting that the system might thermalize in the thermodynamic limit.
Highlights
Understanding the breakdown of ergodicity in the quantum realm is an active and fast growing front of research, motivated by recent developments of controllable quantum simulations which allows one to access out-of-equilibrium dynamics [1,2]
Many-body localization (MBL) describes the paradigm of ergodicity breaking in quantum phases of matter, generalizing the concept of Anderson localization to the interacting case [3,4,5,6]
An many-body localization (MBL) phase is described by an emergent form of integrability, i.e., the existence of a complete set of quasilocal integrals of motion (LIOMs) [7,8,9,10]
Summary
Understanding the breakdown of ergodicity in the quantum realm is an active and fast growing front of research, motivated by recent developments of controllable quantum simulations which allows one to access out-of-equilibrium dynamics [1,2]. An MBL phase is described by an emergent form of integrability, i.e., the existence of a complete set of quasilocal integrals of motion (LIOMs) [7,8,9,10]. These LIOMs are adiabatically connected to the integrals of motion of the noninteracting model and are typically exponentially localized. Transport is absent, some memory of the local structure of its initial state is retained during the quantum evolution, and the interactions between the LIOMs allow a slow information propagation through the system [11,12,13]. The MBL phase should be distinguished from an ergodic or thermal one, in which eigenstates are chaotic and are expected to obey the eigenstate thermalization hypothesis (ETH) [14,15,16,17]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
