Ultraviolet-Infrared Mixing in Marginal Fermi Liquids

Abstract

When Fermi surfaces (FSs) are subject to long-range interactions that are marginal in the renormalization-group sense, Landau Fermi liquids are destroyed, but only barely. With the interaction further screened by particle-hole excitations through one-loop quantum corrections, it has been believed that these marginal Fermi liquids (MFLs) are described by weakly coupled field theories at low energies. In this Letter, we point out a possibility in which higher-loop processes qualitatively change the picture through UV-IR mixing, in which the size of the FS enters as a relevant scale. The UV-IR mixing effect enhances the coupling at low energies, such that the basin of attraction for the weakly coupled fixed point of a $(2+1)$-dimensional MFL shrinks to a measure-zero set in the low-energy limit. This UV-IR mixing is caused by gapless virtual Cooper pairs that spread over the entire FS through marginal long-range interactions. Our finding signals a possible breakdown of the patch description for the MFL and questions the validity of using the MFL as the base theory in a controlled scheme for non-Fermi liquids that arise from relevant long-range interactions.

4.5 pages + references + supplemental material

References in corpus (17)

• U(1) Gauge Theory of the Hubbard Model : Spin Liquid States and Possible Application to k-(BEDT-TTF)_2 Cu_2 (CN)_3
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor kappa-(ET)2Cu2(CN)3
• Continuous Mott transition in semiconductor moiré superlattices
• Quantum Criticality in Twisted Transition Metal Dichalcogenides
• Are non-Fermi-liquids stable to Cooper pairing?
• Theory of a continuous Mott transition in two dimensions
• Gapless spin liquids on the three dimensional hyper-kagome lattice of Na${}_4$Ir${}_3$O${}_8$
• Large $N$ theory of critical Fermi surfaces
• Stability of the U(1) spin liquid with spinon Fermi surface in 2+1 dimensions
• Na4Ir3O8 as a 3D spin liquid with fermionic spinons
• Quasi-Local Strange Metal
• A controlled expansion for certain non-Fermi liquid metals
• Deconfined criticality and a gapless ${\mathbb{Z}}_2$ spin liquid in the square lattice antiferromagnet
• UV/IR Mixing In Non-Fermi Liquids: Higher-Loop Corrections In Different Energy Ranges
• On non-Fermi liquid quantum critical points in heavy fermion metals
• One-dimensional scattering of two-dimensional fermions near quantum criticality

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• Bipartite Fluctuations of Critical Fermi Surfaces
• Effective field theory for ersatz Fermi liquids
• Fermi liquids beyond the forward scattering limit: the role of non-forward scatterings for scale invariance and instabilities
• Infinite critical boson induced non-Fermi liquid in $d=3-\epsilon$ dimensions
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• Disordered non-Fermi liquid fixed point for two-dimensional metals at Ising-nematic quantum critical points
• Ultraviolet/infrared mixing-driven suppression of Kondo screening in the antiferromagnetic quantum critical metal
• Quantum criticality and non-Fermi liquids: the Wilsonian renormalization group perspective
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