Fermi Surface Bosonization for Non-Fermi Liquids

TL;DR

This work develops a frequency-resolved bosonization of the Fermi surface to address non-Fermi liquids in arbitrary dimensions. By introducing a generalized distribution function $f(oldsymbol{ u})$ with a bosonic deformation field $oldsymbol{ amephi}$, the authors construct an effective action whose equation of motion reproduces the collisionless quantum Boltzmann equation, even without well-defined quasiparticles. The quadratic (Gaussian) theory demonstrates forward-scattering cancellation and a clear angular-momentum separation: small-$l$ modes behave like a Fermi liquid while large-$l$ modes exhibit non-Fermi-liquid singularities, consistent with known QBE analyses. The framework extends to all orders in the self-energy, providing a systematic path to study NFL low-energy physics and offering a potential building block for understanding strange metals and related phenomena.

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.

Figures (4)

• Figure 1: Feynmann diagrams for two-point density correlation function.
• Figure 2: Generic vertex correction of the charge response of Fermi surface with a Yukawa coupling to bosonic modes. The full and dotted lines represent fermionic propagators and external vertices, respectively.
• Figure 3: Heuristic procedure to associate $\expval{\delta\hat{\rho}\delta\hat{\rho}}_{\text{off,}1}^{(1)}$ with the Maki-Thomson diagram. A fermionic propagator is first removed from $\Sigma^{R(1)}_0$ (left), and the resulting diagram is then associated with the vertex correction $K$ (right).
• Figure 4: Heuristic procedure to show how $\expval{\delta\hat{\rho}\delta\hat{\rho}}_{\text{off,}n}^{(1)}$ contains the Aslamazov-Larkin diagrams. A fermionic propagator is first removed from $\Sigma^{R(3)}_0$ (left), and the resulting diagram is then associated with the vertex correction $K$ (right).