Theoretical physics · Research notebook
Hello, I’m Maggie.
I study topological quantum matter, strongly correlated systems, non-Abelian quantum geometry, and high-dimensional generalizations of the quantum Hall effect.
“There’s plenty of room at the bottom.” Richard Feynman
Hello! I am Maggie Xheuw, a Ph.D. candidate in Physics at Westlake University, supervised by Prof. Congjun Wu.
My research lies at the intersection of topological phases of matter, quantum many-body systems, and high-dimensional generalizations of quantum Hall effects. I am particularly fascinated by how geometry and topology manifest in strongly correlated electron systems.
Recently, as co-first author, I contributed to a work published in Physical Review Letters (PRL 136, 116501), titled “Incompressible Quantum Hall Liquid on the Four-Dimensional Sphere”[1]. In this work, we formulated microscopic wavefunctions on a four-dimensional sphere inspired by Laughlin's seminal work. Using a generalized pseudopotential framework, we derived an exact microscopic Hamiltonian and demonstrated the existence of an incompressible quantum Hall liquid in four dimensions.
More recently, I have also been working on second-Chern bounds in non-Abelian quantum geometry, where quantum-metric inequalities are connected to non-Abelian Berry curvature and second-Chern topology in four-dimensional parameter spaces [2]. The saturation of the geometric bound reveals a quaternionic structure, providing a higher-dimensional analogue of ideal-band geometry in two-dimensional Chern systems.
What lives in this notebook
This blog is my personal space to share what I learn and connect with fellow researchers. You will find:
- Study notes on quantum field theory, group theory, topology, and mathematical physics.
- Code and computation for numerical simulations, symbolic work, and scientific data analysis.
- Paper reviews and critical discussions of recent preprints and conference lectures.
- Research reflections on academia, productivity, collaboration, and scientific culture.
Selected publications
Incompressible Quantum Hall Liquid on the Four-Dimensional Sphere
Physical Review Letters 136, 116501 (2026)
Second-Chern Bounds in Non-Abelian Quantum Geometry
arXiv:2608.12221 (2026) · Preprint
Geometric bounds linking the quantum metric to non-Abelian Berry curvature and second-Chern topology for doubly degenerate quantum states in four dimensions, with bound saturation tied to a quaternionic geometric structure.
