Hybrid Approach to Non-Equilibrium Control Over Phases of Matter

我们的目标是建立一个多方法的方法来控制非平衡多体相的物质。最重要的是，我们将采用低纠缠技术（张量网络）以及重整化群增强场论工具（泛函RG），我们将进一步推进非平衡领域。我们的具体重点是周期性的驱动（Floquet工程），以及在治疗光物质耦合腔（cavitronics）。两者都是有希望的候选人，以获得更灵活的控制量子多体系统和揭示真正的非平衡现象。该提案的两个项目在方法上是分开的，但在基本的物理问题接口，我们的目标是从两个互补的角度提供一个侵入Floquet工程，cavitronics和其他相关现象。我们相信，这种多方法的方法将是富有成效的，以加深我们的理论认识。这对于特别具有挑战性的二维系统尤其如此。我们的长期目标之一是开发一种新的工具，建立在动态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.