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

[2505.10140] Quantum criticality and non-Fermi liquids: the Wilsonian renormalization group perspective Skip to main content Search Submit Donate Log in Condensed Matter > Strongly Correlated Electrons arXiv:2505.10140 (cond-mat) [Submitted on 15 May 2025 ( v1 ), last revised 30 Jul 2026 (this version, v2)] Title: Quantum criticality and non-Fermi liquids: the Wilsonian renormalization group perspective Authors: Mateusz Homenda , Pawel Jakubczyk , Hiroyuki Yamase View PDF HTML (experimental) Abstract: We develop a theoretical framework based on the nonperturvative 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 wavevector $\vec{Q}=\vec{0}$. 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 protects the system from developing singular bosonic interactions. We emphasize the importance of the nontrivial relative scaling of the bosonic and fermionic cutoffs $\Lambda$ and $\Lambda_f$, which we fix by analyzing the RG flow of the scale-dependent ordering wave-vector $\vec{Q}_\Lambda$. 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 RPA-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 $\vec{Q}=\vec{0}$ and development of a first-order phase transition or a phase characterized by $\vec{Q}\neq\vec{0}$. Subjects: Strongly Correlated Electrons (cond-mat.str-el) ; High Energy Physics - Theory (hep-th) Cite as: arXiv:2505.10140 [cond-mat.str-el] (or arXiv:2505.10140v2 [cond-mat.str-el] for this version) https://doi.org/10.48550/arXiv.2505.10140 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1103/6zxj-zq4c Focus to learn more DOI(s) linking to related resources Submission history From: Mateusz Homenda [ view email ] [v1] Thu, 15 May 2025 10:14:03 UTC (996 KB) [v2] Thu, 30 Jul 2026 09:04:28 UTC (2,297 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.str-el < prev | next > new | recent | 2025-05 Change to browse by: cond-mat hep-th References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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