This project addresses physics questions such as: How does the "arrow of time" emerge from quantum mechanics? How can one characterize chaos in quantum systems with many particles? Does information get lost in a black hole? How can we develop a quantum gravity theory that unifies general relativity and quantum mechanics? These seemingly distinct fundamental questions are all deeply related to the concept of quantum entanglement. In classical mechanics in systems with many particles (many-body systems), because of chaos, it is difficult to predict anything about the future of a complicated system. At the same time, however, the complexity induced by chaos can generate a kind of simplicity that allows us to ignore most details about the individual motion of the particles and describe a many-body system efficiently by macroscopic theories such as hydrodynamics and thermodynamics. This project will investigate how to describe chaos in quantum many-body systems, as opposed to classical many-body systems, and how to relate it to thermodynamics and hydrodynamics. Since the famous work of Bekenstein and Hawking, it has been gradually realized that thermodynamics is also deeply related to another deep mystery of nature, namely gravity. Einstein's general relativity theory describes gravity as a theory of curved and dynamical space-time geometry. This project will investigate how the space-time geometry may emerge as a description of quantum entanglement in many-body systems. The project will provide graduate students with a unique research experience in the interdisciplinary area of quantum information science, high-energy physics and condensed matter physics. The PI will make sustained efforts to introduce the proposed research to undergraduate students and to disseminate the research results of this project beyond the physics community, by lectures, classes and articles.
This project studies quantum chaos and quantum gravity using quantum entanglement. The PI plans to characterize quantum chaos by the nonlocal propagation of quantum information, and generalize the criteria in classical chaos such as Lyapunov exponents to quantum systems. Using entanglement criteria of many-body quantum chaos, the relation of chaos with thermalization of an isolated system will be investigated. Physically, chaos in many-body systems is associated with nonlocal propagation of quantum information, which plays an essential role in thermalization process of an isolated system. In addition to providing a more solid foundation to understand quantum thermalization, the PI plans to further develop a general framework of non-equilibrium dynamics based on the new understanding of quantum chaos. Furthermore, chaos will also be studied using special models that are solvable under certain limit but still preserve chaos. Related to quantum gravity, the PI plans to study holographic duality and quantum gravity using random tensor networks, a framework suitable for describing highly entangled quantum states. With the new language of random tensor networks, it is possible to quantify how entanglement properties are encoded in emergent geometry. Different aspects of the holographic duality will be investigated, including global symmetries, geometrical fluctuation and how Einstein's equations can possibly emerge from entanglement. The PI also plans to apply the new understanding obtained to the long-standing black hole information paradox.
