Geometry · topology · quantum matter
Research programme
Exploring topological phases, strongly correlated quantum systems, and high-dimensional generalizations of the quantum Hall effect.
“The real purpose of science is to understand the deep structure of nature.”
My research focuses on the intersection of condensed matter theory, topological phases, and quantum many-body physics. I am particularly interested in high-dimensional generalizations of the quantum Hall effect and in the ways geometry and topology organize strongly correlated electron systems.
Current directions
Research areas
Topological Phases of Matter
Fractional quantum Hall states, topological order, and symmetry-protected phases in two and four spatial dimensions.
High-Dimensional Quantum Hall Effects
Generalized Laughlin wavefunctions, pseudopotential formalisms, and correlated liquids on higher-dimensional spheres.
Differential Geometry & Topology
Chern–Simons theory, Gauss–Bonnet structures, characteristic classes, and index-theoretic ideas in interacting quantum systems.
Computational Many-Body Physics
Exact diagonalization, Monte Carlo methods, representation theory, and efficient numerical tools for strongly correlated models.
Representative result
Highlighted work
Incompressible Quantum Hall Liquid on the Four-Dimensional Sphere
Phys. Rev. Lett. 136, 116501 (2026)
We constructed microscopic wavefunctions on a four-dimensional sphere, derived an exact pseudopotential Hamiltonian, and established an incompressible fractional quantum Hall liquid in four dimensions—providing a microscopic foundation for high-dimensional quantum Hall physics.
Programme & environment
Collaboration and next questions
Collaborations & facilities
I work closely with the Wu Group at Westlake University, combining analytical field theory, representation-theoretic tools, and large-scale numerical simulations. We also collaborate with experimental groups studying topological materials and quantum devices.
Future directions
- Higher-dimensional generalizations of fractional quantum Hall liquids.
- Connections between geometric invariants and observables in quantum matter.
- Efficient numerical methods for interacting topological systems.
- The role of quantum entanglement in diagnosing topological order.
