Hybrid Approach to Non-Equilibrium Control Over Phases of Matter

我们的目标是建立一种多方法方法来对多体物质相进行非平衡控制。最重要的是，我们将使用低纠缠技术(张量网络)以及重整化群增强型场论工具(泛函RG)，我们将进一步将其推向非平衡领域。我们的重点是周期性驱动(Floquet工程)以及治疗腔中的光-物质耦合(空电子学)。两人都很有希望获得对量子多体系统的更灵活的控制，并揭示真正的非平衡现象。本提案的两个项目在方法上是分开的，但在潜在的物理问题上是相互联系的，我们的目标是从两个互补的角度深入了解Floquet工程、空电子学和其他相关现象。我们相信，这样的多方法方法将有助于深化我们的理论理解。这一点对二维系统尤其适用，因为它们特别具有挑战性。我们的长期目标之一是开发一种新的工具，它建立在动力平均场理论的基础上，并为我们的多方法工具带增加另一个角度。

Our goal is to establish a multi-method approach to non-equilibrium control over many-body phases of matter. Most importantly, we will employ low-entanglement techniques (tensor networks) as well as renormalization-group enhanced field-theoretical tools (functional RG), which we will push further into the non-equilibrium realm. Our specific focus is on periodic driving (Floquet engineering) as well as on treating the light-matter coupling in a cavity (cavitronics). Both are promising candidates to obtain a more flexible control over quantum many-body systems and to unveil true non-equilibrium phenomena. The two projects of this proposal are methodologically separated but interface at the underlying physical problems, and we aim at providing an inroad into Floquet engineering, cavitronics, and other related phenomena from two complementary angles. We believe that such a multi-method approach will be fruitful to deepen our theoretical understanding. This holds especially true for two-dimensional systems, which are particularly challenging. One of our long-term goals it to develop a novel tool that builds on the dynamical mean field theory and that adds another angle to our multi-method tool belt.