Phase transitions, criticality and non-trivial topological states in non-equilibrium driven-dissipative systems using analytical methods and tensor ne

本论文将探讨非平衡驱动耗散量子系统的相变、临界性和非平凡拓扑态的分类。特别是，本论文将着重于强相互作用的光-物质系统，如激子-极化激元晶格，它们支持丰富的现象，如高温玻色-爱因斯坦凝聚，超流和量子涡旋。本论文将通过发展分析技术，如重整化群，平均场理论和Keldysh场论，以及使用计算模拟，如张量网络方法，特别是无限2D张量网络。

The thesis will explore the classification of phase transitions, criticality and non-trivial topologicalstates in non-equilibrium driven-dissipative quantum systems. In particular, the thesis will focus onstrongly interacting light-matter systems such as exciton-polariton lattices which support rich phenomenasuch as high temperature Bose-Einstein condensation, superfluidity and quantum vortices.The thesis will characterise open driven-dissipative quantum systems by developing analytical techniques,such as renormalisation group, mean-field theory and Keldysh field theory, and the use ofcomputational simulations such as tensor network methods, specifically infinite 2D tensor networksiPEPS.