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Bloch's theorem is the centerpiece of topological band theory, which itselfhas defined an era of quantum materials research. However, Bloch's theorem isbroken by a perpendicular magnetic field, making it difficult to studytopological systems in strong flux. For the first time, moir\'e materials havemade this problem experimentally relevant, and its solution is the focus ofthis work. We construct gauge-invariant irreps of the magnetic translationgroup at $2\pi$ flux on infinite boundary conditions, allowing us to giveanalytical expressions in terms of the Siegel theta function for the magneticBloch Hamiltonian, non-Abelian Wilson loop, and many-body form factors. Weillustrate our formalism using a simple square lattice model and theBistritzer-MacDonald Hamiltonian of twisted bilayer graphene, obtainingreentrant ground states at $2\pi$ flux under the Coulomb interaction.

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