Almost strong ( 0,π ) edge modes in clean interacting one-dimensional Floquet systems

Abstract

Certain periodically driven quantum many-particle systems in one dimension are known to exhibit edge modes that are related to topological properties and lead to approximate degeneracies of the Floquet spectrum. A similar situation occurs in spin chains, where stable edge modes were shown to exist at all energies in certain integrable spin chains. Moreover, these edge modes were found to be remarkably stable to perturbations. Here we investigate the stability of edge modes in interacting, periodically driven, clean systems. We introduce a model that features edge modes that persist over times scales well in excess of the time needed for the bulk of the system to heat to infinite temperatures.

Strong and almost strong modes of Floquet spin chains in Krylov subspaces

“…In this section we introduce the integrable model of the Floquet chain. We consider an open chain of length L where the stroboscopic time evolution is generated by the following Floquet unitary [20,22,23,28,29]…”

“…Under Floquet driving, besides the SZMs, new edge modes arise [18][19][20][21][22], which are called strong π modes (SPMs) [22], with the possibility of having phases where SZMs and SPMs co-exist [22][23][24][25][26]. In order to define the strong modes in a Floquet system, one needs to adapt the previous definition of the SZM to that of a Floquet unitary over one drive cycle, U .…”

“…In the Floquet setting, SZMs and SPMs have been identified in free fermion (integrable) Floquet chains [18,20,22]. In addition, the effect of weak interactions were explored using exact diagonalization (ED) where it was found that quasi-stable and long lived edge modes exist despite bulk heating [22]. Drawing inspiration from the static case [13], these quasi-stable modes are called ASZMs and almost strong π modes (ASPMs) [22].…”

“…In addition, the effect of weak interactions were explored using exact diagonalization (ED) where it was found that quasi-stable and long lived edge modes exist despite bulk heating [22]. Drawing inspiration from the static case [13], these quasi-stable modes are called ASZMs and almost strong π modes (ASPMs) [22]. The current paper proposes a route to understanding these quasi-stable modes by mapping their dynamics to a Krylov subspace.…”

Floquet Engineering Topological Many-Body Localized Systems

“…Most of the proposals on how topology, disorder, and Floquet engineering can be exploited in the design of quantum devices [14][15][16][17][18][19][20][21][22][23][24][25] either concentrate on one or two of these phenomena separately or use special models. Floquet engineering has been suggested as a route to realizing effective topological systems [26][27][28][29][30][31][32], but those studies neglect two-body interactions and thus ignore the fact that a generic driven system will heat up [33].…”