Periodically Driven Many-Body Systems

远离热平衡的量子多体系统自然而然地出现在从凝聚态到宇宙学的各种物理学学科中。近年来，量子多体系统的动力学演化一直是人们关注的焦点，量子多体系统与环境完全隔离。特别是，在周期性驱动的系统中，可能会出现非驱动系统所没有的奇异现象。例如，已经证明了在驱动周期的整数倍处表现出持续振荡的Floket时间晶体，并提出了某些对称性保护的拓扑相。除了阶段的实现之外，在本项目的第一个资助期发现，周期性驱动的多体系统的加热动力学可以在Floquet预热状态下的中间时间尺度上强烈地减少，或者甚至可以在强烈无序的多体局域系统中完全停止。受这些发现的启发，我们在这个后续项目中的目标如下：(I)我们将确定不同类型的强关联多体系统的加热动力学。为此，我们将发展一个Floquite Boltzmann动力学方程来研究O(N)场理论中的能量吸收到极晚的时间，这在我们以前的方法中是无法获得的。我们还将考虑弱相互作用玻色子，并将后期加热动力学与非微扰O(N)场理论进行比较，后者给出了时间行为的奇异平方根的暗示。此外，我们还将研究周期驱动的Sachdev-Ye-Kitaev模型的动力学，该模型描述了一种非费米液体，可以用不规则形状的石墨烯薄片在强磁场中实验实现。(Ii)我们将考虑一个可积的海森堡链，并用精确的数值方法和广义流体力学的思想研究运动积分在加热动力学中的作用。(Iii)我们将提出并研究在周期驱动的超冷Rydberg链中实现新颖的Floket对称性保护的拓扑相。通过这个项目，我们将能够识别非平衡动力学中的普遍特征，并开发出有趣的实验路线，在周期驱动的多体系统中实现奇异的远离平衡的量子态。

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.