Fermi Surface Bosonization for Non-Fermi Liquids

TL;DR

This paper introduces a bosonization method for Fermi surfaces applicable to non-Fermi liquids, enabling analysis of complex, gapless systems without relying on well-defined quasiparticles, thus advancing understanding of strange metals.

Contribution

It develops a bosonization procedure that does not depend on sharp excitations, suitable for analyzing non-Fermi liquids in any dimension.

Findings

Reproduces collisionless quantum Boltzmann equation from an effective action.

Applicable to any dimension and Fermi surface shape.

Provides a new analytical tool for studying strange metals.

Abstract

Understanding non-Fermi liquids in dimensions higher than one remains one of the most formidable challenges in modern condensed matter physics. These systems, characterized by an abundance of gapless degrees of freedom and the absence of well-defined quasiparticles, defy conventional analytical frameworks. Inspired by recent work [Delacretaz, Du, Mehta, and Son, Physical Review Research, 4, 033131 (2022)], we present a procedure for bosonizing Fermi surfaces that does not rely on the existence of sharp excitation and is thus directly applicable to non-Fermi liquids. Our method involves parameterizing the generalized fermionic distribution function through a bosonic field that describes frequency-dependent local variations of the chemical potential in momentum space. We propose an effective action that produces the collisionless quantum Boltzmann equation as its equation of motion and can be used for any dimension and Fermi surface of interest. Even at the quadratic order, this action reproduces non-trivial results obtainable only through involved analysis with alternative means. By offering an alternative method directly applicable to studying the low-energy physics of Fermi and non-Fermi liquids, our work potentially stands as an important building block in advancing the comprehension of strange metals and associated phenomena.