Bosonization of Fermi liquids in a weak magnetic field

TL;DR

This paper extends two-dimensional bosonization techniques to Fermi liquids in a weak magnetic field, enabling non-perturbative analysis of quantum oscillations and collective modes in strongly correlated electronic systems.

Contribution

It introduces a covariant Schwinger algebra for particle-hole fluctuations and develops a bosonization formalism for Fermi liquids under a weak magnetic field, including interactions.

Findings

Derivation of a covariant Schwinger algebra for particle-hole fluctuations.

Reproduction of de Haas-van Alphen oscillations and Lifshitz-Kosevich theory.

Oscillatory corrections to Landau zero sound mode due to interactions.

Abstract

Novel controlled non-perturbative techniques are a must in the study of strongly correlated systems, especially near quantum criticality. One of these techniques, bosonization, has been extensively used to understand one-dimensional, as well as higher dimensional electronic systems at finite density. In this paper, we generalize the theory of two-dimensional bosonization of Fermi liquids, in the presence of a homogeneous weak magnetic field perpendicular to the plane. Here, we extend the formalism of bosonization to treat free spinless fermions at finite density in a uniform magnetic field. We show that particle-hole fluctuations of a Fermi surface satisfy a {\em covariant Schwinger algebra}, allowing to express a fermionic theory with forward scattering interactions as a quadratic bosonic theory representing the quantum fluctuations of the Fermi surface. By means of a coherent-state path integral formalism we compute the fermion propagator as well as particle-hole bosonic correlations functions. We analyze the presence of de Haas-van Alphen oscillations and show how the quantum oscillations of the orbital magnetization, the Lifshitz-Kosevich theory, are obtained by means of the bosonized theory. We also study the effects of forward scattering interactions. In particular, we obtain oscillatory corrections to the Landau zero sound collective mode.