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We develop a theoretical framework based on the nonperturbative renormalization group (RG) in the one-particle irreducible (Wetterich) formulation to tackle the interplay of coupled fermionic and order-parameter fluctuations at metallic quantum critical points (QCPs) with ordering wave vector Q⃗ = 0⃗. 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 protects the system from developing singular bosonic interactions. We emphasize the importance of the nontrivial relative scaling of the bosonic and fermionic cutoffs Λ and Λ_f, which we fix by analyzing the RG flow of the scale-dependent ordering wave-vector Q⃗_Λ. Upon neglecting Fermi self-energy in the loop integrals of the functional RG flow, we identify a non-Fermi liquid RG fixed point and recover the features obtained earlier within random phase approximation-type approaches. In a subsequent step, we self-consistently include the scaling of the self-energy and the Yukawa coupling. We find a generic instability of the non-Fermi liquid RG fixed point. This implies, at least at this truncation level, absence of the QCP with Q⃗ = 0⃗ and development of a first-order phase transition or a phase characterized by Q⃗ ≠ 0⃗.

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• In Copyright
  

  ©2026 American Physical Society

Keyword: Quantum criticality, Landau damping, Renormalization group, non-Fermi liquid

Date published: 2026-08-24

Publisher: American Physical Society (APS)

Journal:

• Physical Review B (ISSN: 1550235X) vol. 114 issue. 10 105134

Funding:

• Japan Society for the Promotion of Science JP20H01856
• Ministry of Education, Culture, Sports, Science and Technology
• Polish National Science Center 2021/43/B/ST3/01223

Manuscript type: Author's version (Accepted manuscript)

MDR DOI: https://doi.org/10.48505/nims.6514

First published URL: https://doi.org/10.1103/6zxj-zq4c

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Updated at: 2026-09-11 10:16:57 +0900

Published on MDR: 2026-09-11 14:26:00 +0900