Non-Fermi liquid induced by U(1) gauge field interactions: a functional renormalization group analysis

TL;DR

This paper investigates a non-Fermi-liquid state in a two-dimensional Fermi gas interacting with a U(1) gauge field using functional renormalization group methods, revealing new critical exponents and scaling behaviors.

Contribution

It introduces a gauge-symmetry-aware fRG scheme and provides novel insights into the critical exponents and scaling in the non-Fermi-liquid phase.

Findings

Critical exponents are largely insensitive to gauge symmetry constraints.

The gauge-boson mass term is RG-relevant without constraints and irrelevant with constraints.

The fermion self-energy scales as ()^{1/2} with dynamical exponent z=2.

Abstract

We study the non-Fermi-liquid state formed by an isotropic, degenerate Fermi gas in two spatial dimensions interacting with a U(1) gauge field. Our calculation uses the functional renormalization group (fRG) with a soft frequency cutoff for the fermions. The fRG scheme we employ takes account of the gauge symmetry, which imposes relations (modified Ward-Takahashi identities) between the couplings which constrain the RG flow. The critical exponents and couplings we find for the resulting non-Fermi liquid are mostly insensitive to whether or not we enforce the gauge symmetry constraints, which signifies either that the constraints are superfluous or that the frequency-cutoff scheme is particularly robust. The exception is the gauge-boson mass term, which is RG-relevant about the fixed point without the constraints, but is irrelevant when they are enforced. The latter is physically accurate, as a gauge symmetry cannot be spontaneously broken. In addition, we find $z=2$ and $\Sigma(\omega,k_F)\sim\omega^{1/2}$ for the boson dynamical exponent and scaling of the fermion self-energy, respectively. These results differ considerably from those of past works on the model, though we argue for their plausibility.