Broadly speaking, my research interests pertain to emergent collective phenomena in quantum many-body systems.
Quantum spin liquids are exotic phases of matter that arise when strong quantum fluctuations in spin systems prevent the emergence of conventional order at zero temperature. These states have garnered considerable interest due to their many surprising features, such as emergent anyon excitations and topological order. I am interested in several aspects of this, such as
Coexistence of spin liquids with charge fluctuations or metallic phases
Phase transitions between spin liquids and conventionally ordered phases
Interplay between global symmetries and topological order
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
An unavoidable feature in any physical realization of a quantum system is the coupling of its degrees of freedom to the environment. Although these interactions tend to act destructively on the physics of the isolated system, it is also possible to leverage the dissipative nature of these couplings to engineer intrinsically non-equilibrium behavior or as an efficient way of preparing quantum states. My interests in this topic include
Interplay between fractionalization and thermalization in strongly-correlated quantum systems
Exactly solvable models of open quantum dynamics
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
Variational wavefunctions for topologically-ordered phases