Floquet physics and Lattice fermions

Abstract

Different subfields of physics sometimes share a common thread which is often recognized only in hindsight. I will briefly highlight such an example from the past pointing to ties between lattice QCD and condensed matter physics. I will then share recent developments which suggest that similar ties may exist between a class of non-equilibrium quantum systems known as Floquet insulators and discrete time lattice fermion theories. Floquet insulators are periodically driven quantum systems that can host novel non-equilibrium phases as a function of the drive parameters. I will show that the spectrum of a certain 1+1 dimensional Floquet system can be replicated exactly using a discrete time static relativistic fermion and how such correspondence may be extended to higher dimensions.