Magnetic Bloch Theorem and Reentrant Flat Bands in Twisted Bilayer Graphene at $2\pi$ Flux

Bloch's theorem is the centerpiece of topological band theory, which itself has defined an era of quantum materials research. However, Bloch's theorem is broken by a perpendicular magnetic field, making it difficult to study topological systems in strong flux. For the first time, moir\'e materials have made this problem experimentally relevant, and its solution is the focus of this work. We construct gauge-invariant irreps of the magnetic translation group at $2\pi$ flux on infinite boundary conditions, allowing us to give analytical expressions in terms of the Siegel theta function for the magnetic Bloch Hamiltonian, non-Abelian Wilson loop, and many-body form factors. We illustrate our formalism using a simple square lattice model and the Bistritzer-MacDonald Hamiltonian of twisted bilayer graphene, obtaining reentrant ground states at $2\pi$ flux under the Coulomb interaction.