Broadly speaking, my research interests pertain to emergent collective phenomena in quantum many-body systems.
In contrast to conventional phases of matter, which are identified by the spontaneous breaking of global symmetries, topologically-ordered phases of matter are distinguished through non-local order parameters and emergent anyon excitations. These phases support a plethora of exotic phenomena, including unconventional instabilities and phase transitions. My interests in this field include
Interplay between global symmetries and topological order
Mechanisms for topological order, such as the fractional quantum anomalous Hall effect, in 2D materials
Superconducting instabilities in topologically-ordered phases
Topological order in frustrated magnetic systems
A remarkable feature of phase transitions is the universal properties of their critical points that emerge at large scales, insensitive to microscopic details. For transitions driven by quantum fluctuations rather than thermal, this is manifest by long-range quantum entanglement. This high degree of entanglement can lead to manifestly non-classical behavior that persists across a range of temperatures. I am excited by subjects such as
Deconfined criticality in quantum spin models
UV/IR mixing and unconventional scaling behavior in critical theories
Disordered quantum criticality
The difficulty of simulating large-scale strongly-interacting quantum systems is a major obstacle in uncovering the nature of uniquely quantum phenomenon. A close dialogue between analytic and numerical techniques is important for discovering new quantum many-body phenomena. In this direction, problems that I am interested in include
Sign-problem-free (efficiently simulatable) models of quantum criticality
Applications of neural networks to quantum many-body simulations, including neural quantum states and Monte Carlo methods