Sang, Shengqi2024-06-242024-06-242024-06-242024-06-18http://hdl.handle.net/10012/20680The thesis is divided into two parts, both focusing on the topic of open quantum many-body systems. The first part explores the properties of quantum circuits interspersed with measurements. Tuned by the frequency of measurements, the circuit exhibits two stable dynamical phases: a weakly-monitored phase and a strongly-monitored one. For the former case, we analyze its non-equilibrium properties and unveil that it exhibits physical length scales that grow super-linearly with time. For the latter case, we demonstrate that it can maintain non-trivial quantum order when symmetries are present. The second part addresses phases of matter for mixed many-body states. We propose a real-space renormalization group approach for mixed states and apply it to derive phase diagrams for various examples. For decohered topological codes, we establish a precise relationship between the decodability and the topological phase transitions. Lastly, we introduce the notion of 'Markov length', a length scale that measures the locality of correlation, as a diagnostic for the stability of mixed state phases.enphysicsDoctoral Thesis