Topology and Broken Symmetry in Floquet Systems

TL;DR

This paper reviews how Floquet systems, despite their time-dependent drives that could cause heating, can exhibit nontrivial topological phases and exotic behaviors, including stability of many-body Floquet phases.

Contribution

It synthesizes recent advances in understanding topological and symmetry-breaking phenomena in driven Floquet systems, highlighting novel phases and stability mechanisms.

Findings

Floquet drives can host nontrivial topology in single-particle systems

Existence of exotic Floquet phases in interacting systems

Many-body Floquet phases can be stable against heating

Abstract

Floquet systems are governed by periodic, time-dependent, Hamiltonians. Prima facie they should absorb energy from the external drives involved in modulating their couplings and heat up to infinite temperature. However this unhappy state of affairs can be avoided in many ways. Instead, as has become clear from much recent work, they can exhibit a variety of nontrivial behavior---some of it impossible in undriven systems. In this review we describe the main ideas and themes of this work: novel Floquet drives which exhibit nontrivial topology in single-particle systems, the existence and classification of exotic Floquet drives in interacting systems, and the attendant notion of many-body Floquet phases and arguments for their stability to heating.