Effective field theory of Berry Fermi liquid from the coadjoint orbit method

TL;DR

This paper develops an effective field theory for Berry Fermi liquids incorporating Berry curvature and interactions, enabling the calculation of electrical responses and confirming the anomalous Hall effect.

Contribution

It introduces a covariant phase space formalism for Berry Fermi liquids using the coadjoint orbit method, extending previous theories to include time dependence and interactions.

Findings

Derived the effective action for Berry Fermi liquids.

Computed linear and nonlinear electrical responses.

Confirmed the anomalous Hall effect via kinetic theory.

Abstract

We construct an effective field theory for an interacting Fermi liquid with nonzero Berry curvature at zero temperature, called the Berry Fermi liquid. We start with the extended phase space formalism, incorporating physical time into the configuration space. This approach allows us to include the time dependence of the background gauge fields ``covariantly'' into the symplectic structure. Upon restricting to the physical hypersurface, the effective action that lives on the coadjoint orbit becomes the minus free energy on the extended phase space. We also derive the action perturbatively in external fields using the canonical variables. For applications, we compute both linear and nonlinear electrical responses using the Kubo formula, and identify contributions from the electric and magnetic dipole moments, which stem from interactions breaking parity and time-reversal symmetry. The anomalous Hall effect is confirmed using the kinetic theory.