Coadjoint-orbit Bosonization of Multi-band Fermions: Application to de Haas-van Alphen Oscillations and More

Using the method of coadjoint orbits, we develop a bosonized effective field theory (EFT) for a multi-band fermionic system in a weak magnetic field. In the bosonic theory, the base manifold is the phase space and the target manifold is the fluctuating single-particle distribution function as coadjoint orbits of canonical transformations. We present a systematic procedure to project the field theory to a single band perturbatively in B, where the Berry phase effects naturally emerge at the leading order in B. In particular, we consider the de Haas-van Alphen effect of a 2d Fermi pocket, and obtain the modification to the oscillation phase and amplitude due to the Berry phase. Higher order effects in B will also be discussed.