Field-theoretic functional renormalization group formalism for non-Fermi liquids and its application to the antiferromagnetic quantum critical metal in two dimensions

Abstract

To capture the universal low-energy physics of metals within effective field theories, one has to generalize the usual notion of scale invariance and renormalizable field theory due to the presence of intrinsic scales (Fermi momenta). In this paper, we develop a field-theoretic functional renormalization group formalism for full low-energy effective field theories of non-Fermi liquids that include all gapless modes around the Fermi surface. The formalism is applied to the non-Fermi liquid that arises at the antiferromagnetic quantum critical point in two space dimensions. In the space of coupling functions, an interacting fixed point arises at a point with momentum-independent couplings and vanishing nesting angle. In theories deformed with non-zero nesting angles, coupling functions acquire universal momentum profiles controlled by the bare nesting angles at low energies before flowing to superconducting states in the low-energy limit. The superconducting instability is unavoidable because lukewarm electrons that are coherent enough to be susceptible to pairing end up being subject to a renormalized attractive interaction with its minimum strength set by the nesting angle. Despite the inevitable superconducting instability, theories with small bare nesting angles and bare four-fermion couplings that are repulsive or weakly attractive must pass through the region with slow RG flow due to the proximity to the non-Fermi liquid fixed point. The bottleneck region controls the scaling behaviours of the normal state and the quasi-universal pathway from the non-Fermi liquid to superconductivity. In the limit that the nesting angle is small, the non-Fermi liquid scaling dictates the physics over a large window of energy scale above the superconducting transition temperature.

109 pages

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• Space of non-Fermi liquids
• Unconventional Gross-Neveu quantum criticality: Interaction-induced SO(3)-biadjoint insulator and emergent SU(3) symmetry
• Fermi liquids beyond the forward scattering limit: the role of non-forward scatterings for scale invariance and instabilities
• Strange metallicity in an antiferromagnetic quantum critical model: A sign-problem-free quantum Monte-Carlo study
• Quantum $z=2$ Lifshitz criticality in one-dimensional interacting fermions
• Ultraviolet/infrared mixing-driven suppression of Kondo screening in the antiferromagnetic quantum critical metal
• Emergence of curved momentum-spacetime and its effect on the cyclotron motion in the antiferromagnetic quantum critical metal
• Anomalous quasiparticle lifetime in geometric quantum critical metals
• Dynamical kinetic energy quenching in the antiferromagnetic quantum critical metals