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

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 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>z</a:mi><a:mo>=</a:mo><a:mn>2</a:mn></a:mrow></a:math> and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi mathvariant="normal">Σ</b:mi><b:mrow><b:mo>(</b:mo><b:mi>ω</b:mi><b:mo>,</b:mo><b:msub><b:mi>k</b:mi><b:mi>F</b:mi></b:msub><b:mo>)</b:mo></b:mrow><b:mo>∼</b:mo><b:msup><b:mi>ω</b:mi><b:mrow><b:mn>1</b:mn><b:mo>/</b:mo><b:mn>2</b:mn></b:mrow></b:msup></b:mrow></b:math> 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.