I am currently focusing on the following topics
Exotic phases in quantum magnets:
Quantum magnetic systems form a fertile ground for both theoretical and experimental studies of exotic quantum phases of matter. I am particularly interested in a class of quantum magnetic phases, often referred to as spin liquids, that host exotic quasi-particle excitations whose quantum numbers and statistics take fractional values compared to the microscopic constituents of the system. Theoretical understandings of the inner working of such phases and of the signature of the emergent fractionalized excitation are crucial for the identification of these phases in experimental systems. Even though these exotic quantum phases with fractionalized excitations often emerge in strongly interacting quantum magnets, we can still use non-perturbative approaches to study their behavior. For example, some properties of the fractionalized excitations are fundamentally constrained by the spin and the crystal symmetries of the quantum magnets. Such constraints can sometimes have non-trivial implications for nearby phases and even for the whole phases diagram of the quantum magnet.
Strongly-interacting quantum critical points and gapless quantum matters:
Strong interactions can lead to many exotic quantum critical points and gapless quantum matters. At the same time, strong interactions often render standard approaches based on the perturbation theory ineffective, making it harder to tackle these critical points and gapless phases analytically. In some of these scenarios, non-perturbative approach methods are very helpful as they provide vital information about the universal behavior of the strongly interacting quantum systems and sometimes even provide exact solutions to the problems. For example, dualities and quantum anomalies are useful tools to obtain universal properties of strongly-interacting quantum critical points in quantum magnets and in fractional quantum Hall systems. Dynamical mean-field theories can be applied to obtain the exact solutions of a large class of non-Fermi liquids, a type of gapless metallic states without any quasi-particles. I am generally interested in the development and the application of non-perturbative approaches to strongly-interacting quantum critical points and gapless quantum matters.
The dynamics of quantum entanglement is the key to the understanding of many important questions like how generic systems reach thermal equilibrium and how quantum information spreads under the unitary evolution of many-body systems. It has been found that quantum systems can enter different dynamical phases with different entanglement scaling. I am interested in developing the tools to understand the phase transitions between these different dynamical phases. I am also interested in the evolution of quantum entanglement in many-body systems that exhibit quantum chaos.
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