Geometric Aspects of Quantum Matter

'Topology' and 'geometry' are an important math concepts that have influenced the modern condensed matter physics. 'Topology' determines the global aspects of quantum matters such as classification, Hall conductivity, robust edge states etc. In contrast, 'geometry' is local and determines the details of electrons' coherence, the stability, and how they response to external probes.

I am particularly interested in how the quantum geometries of the Bloch wavefunction influence the stabilities of interacting phase, and contribute to the development of Theory of Ideal Flatbands [1,2] and generalized Landau levels [4].

My recent seminar talk on this topic titled "Quantum Geometric Aspects of Chiral Twisted Graphene Models" at CMSA Harvard is available on YouTube! Video link here.

[1] Jie Wang, Jennifer Cano, Andrew J. Millis, Zhao Liu and Bo Yang (2021). Exact Landau Level Description of Geometry and Interaction in a Flatband. PhysRevLett.127.246403

[2] Jie Wang and Zhao Liu (2021). Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models. arXiv:2109.10325 (PRL accepted, Editor's Suggestion)

[3] Jie Wang, Semyon Klevtsov and Zhao Liu (2022). Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra. arXiv: 2210.013487.

[4] Zhao Liu*, Bruno Mera*, Manato Fujimoto, Tomoki Ozawa and Jie Wang (2024). Theory of Generalized Landau Levels and Implication for non-Abelian States. arXiv: 2405.14479.