Periodically Driven Many-Body Systems

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Quantum many-body systems far from thermal equilibrium arise naturally in a variety of disciplines of physics, ranging from condensed matter to cosmology. In recent years, there has been an intense focus on understanding the dynamical evolution of quantum many-body systems that are well isolated from their environment. Particularly, in periodically driven systems exotic phenomena can emerge that are absent in their undriven counterparts. For example, Floquet time crystals which exhibit persistent oscillations at integer multiples of the driving period have been demonstrated and certain symmetry protected topological phases have been proposed. Beyond the realization of phases it has been found in the first funding period of this project, that the heating dynamics of periodically driven many-body systems can be strongly reduced on intermediate time scales in Floquet prethermal states or can even come to a full stop in strongly disordered many-body localized systems. Motivated by these findings, our goals in this follow-up project are as follows: (i) We will determine the heating dynamics for different types of strongly correlated many-body systems. To this end, we will develop a Floquet Boltzmann kinetic equation to study the energy absorption in the O(N) field theory to extremely late times which were not accessible in our previous approach. We will also consider weakly interacting bosons and compare the late time heating dynamics with the non-perturbative O(N) field theory, which gave hints for an exotic square root in time behavior. Moreover, we will study the dynamics of the periodically driven Sachdev-Ye-Kitaev model, which describes a non-Fermi liquid and may be experimentally realized with irregularly shaped Graphene flakes in strong magnetic fields. (ii) We will consider an integrable Heisenberg chain and investigate the role of integrals of motion on the heating dynamics using exact numerical methods and ideas from generalized hydrodynamics. (iii) We will propose and study the realization of novel Floquet symmetry protected topological phases in periodically driven ultracold Rydberg chains. With the approach of this project, we will be able to identify universal features in the non-equilibrium dynamics and develop fascinating experimental routes to realize exotic far-from equilibrium quantum states in periodically driven many-body systems.