This article aims to briefly introduce the theoretical and experimental detection methods related to “chiral graviton” excitations in fractional quantum Hall liquids, providing material for the recent heated discussions in related fields. My ability is limited, so I welcome any corrections from experts.

This note aims to elucidate the connection between the conductivity of a many-body system and the quantum geometry of its ground state, and to explain how to distinguish between conductors and insulators solely based on the “locality” of the ground state wavefunction.

This note briefly describes the gauge selection problem of Maximally Localized Wannier Functions and discusses how Quantum Geometry limits their localization.

This article aims to introduce the mean field approximation while elucidating its variational nature.

Hartree, Fock, and BCS—these individual mean field approximations appear to be mutually incompatible decoupling methods. However, by leveraging the variational nature of the mean field approximation, we discover that they can indeed be mixed 1:1:1.

This article aims to clarify the consistency between Fermi’s Golden Rule and Joule Heat.

This article aims to derive the nonlinear response theory of the Kubo Formula.