Quantum criticality and non-Fermi liquids: the nonperturbative renormalization group perspective

TL;DR

This paper develops a nonperturbative renormalization group framework to analyze quantum critical points with coupled fermionic and bosonic fluctuations, revealing non-Fermi liquid behavior and fixed points different from traditional RPA predictions.

Contribution

It introduces a comprehensive RG approach that treats fermionic and bosonic fluctuations on equal footing, providing new insights into non-Fermi liquid scaling at metallic quantum critical points.

Findings

Fermi self-energy scaling exponent approximately 0.50

Bosonic dynamical exponent around 2

Fixed points differ from RPA predictions

Abstract

We develop a thorough theoretical framework based on the nonperturvative renormalization group (RG) a la Wetterich to tackle the interplay of coupled fermionic and order-parameter fluctuations at metallic quantum critical points with ordering wavevectors $\vec{Q}=\vec{0}$. We consistently treat the dynamical emergence of the Landau damping of the bosonic mode and non-Fermi liquid scaling of fermions upon lowering the cutoff scale. The loop integrals of the present theory involve only contributions from fluctuations above the cutoff scale, which drive the system to a non-Fermi liquid RG fixed point of different scaling properties from those obtained within the random phase approximation (RPA) or expansions around it. In particular the scaling exponent for the Fermi self-energy acquires the value $\alpha\approx 0.50$ rather than the anticipated $\alpha\approx 0.66$, while the bosonic dynamical exponent $z\approx 2$. We demonstrate how results characteristic for the RPA-type fixed-point scaling are recovered in our framework by a questionable procedure of removing the fermionic cutoff much faster than the bosonic one.