Berry Fermi Liquid Theory

TL;DR

This paper extends Landau Fermi liquid theory to include Berry curvature effects, providing a kinetic framework that matches quantum field theory results for electromagnetic responses in interacting fermion systems.

Contribution

It introduces a novel kinetic equation and current relation for Berry Fermi liquids, bridging microscopic quantum field theory and macroscopic response descriptions.

Findings

Kinetic theory accurately describes electromagnetic responses with Berry curvature.

Perturbative quantum field theory results match kinetic theory predictions.

The framework applies to a broad class of interacting fermion systems.

Abstract

We develop an extension of the Landau Fermi liquid theory to systems of interacting fermions with non-trivial Berry curvature. We propose a kinetic equation and a constitutive relation for the electromagnetic current that together encode the linear response of such systems to external electromagnetic perturbations, to leading and next-to-leading orders in the expansion over the frequency and wave number of the perturbations. We analyze the Feynman diagrams in a large class of interacting quantum field theories and show that, after summing up all orders in perturbation theory, the current-current correlator exactly matches with the result obtained from the kinetic theory.