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

Borges, Francisco; Borissov, Anton; Singh, Rajesh; Schlief, Andrés; Lee, Sung-Sik

doi:10.1016/j.aop.2023.169221

Cited by 12 publications

(5 citation statements)

References 93 publications

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“…Specifically, our search is focused on the important class of non-Fermi liquids described by the Hertz-Millis framework, where gapless bosonic order parameter fields with zero crystal momentum couple strongly to a Fermi surface. Although we have not yet considered finite-momentum order parameters, there has been much recent progress in studying that class of theories [82,83].…”

Section: Discussionmentioning

confidence: 99%

Loop current fluctuations and quantum critical transport

et al. 2023

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We study electrical transport at quantum critical points (QCPs) associated with loop current ordering in a metal, focusing specifically on models of the “Hertz-Millis” type. At the infrared (IR) fixed point and in the absence of disorder, the simplest such models have infinite DC conductivity and zero incoherent conductivity at nonzero frequencies. However, we find that a particular deformation, involving NN species of bosons and fermions with random couplings in flavor space, admits a finite incoherent, frequency-dependent conductivity at the IR fixed point, \sigma(\omega>0)\sim\omega^{-2/z}σ(ω>0)∼ω−2/z, where zz is the boson dynamical exponent. Leveraging the non-perturbative structure of quantum anomalies, we develop a powerful calculational method for transport. The resulting "anomaly-assisted large NN expansion" allows us to extract the conductivity systematically. Although our results imply that such random-flavor models are problematic as a description of the physical N = 1N=1 system, they serve to illustrate some general conditions for quantum critical transport as well as the anomaly-assisted calculational methods. In addition, we revisit an old result that irrelevant operators generate a frequency-dependent conductivity, \sigma(\omega>0) \sim \omega^{-2(z-2)/z}σ(ω>0)∼ω−2(z−2)/z, in problems of this kind. We show explicitly, within the scope of the original calculation, that this result does not hold for any order parameter.

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Section: Discussionmentioning

confidence: 99%

Loop current fluctuations and quantum critical transport

et al. 2023

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“…In metals, the degree of IR singularity that a coupling can create does not necessarily match its scaling dimension because of the scale associated with the Fermi momentum. Consequently, the notion of renormalizable field theory needs to be generalized for metals [54]. Second, k F has scaling dimension 1 and runs toward infinity in the low-energy (s → 0) limit.…”

Section: Local Effective Field Theorymentioning

confidence: 99%

“…The phase space measured in the unit µ increases with decreasing µ. This extensive phase space is what promotes the quartic coupling to the marginal coupling although it has scaling dimension −1 [54]. One can incorporate the phase space to define a new dimensionless coupling function as…”

Section: Nearly Forward Scatteringmentioning

confidence: 99%

“…In this work, we use the field-theoretic functional renormalization group scheme to describe Landau Fermi liquid and its instabilities within the frame work of renormalizable local effective field theory [54]. The key ingredient of our work is the non-forward scatterings.…”

Section: Introductionmentioning

confidence: 99%

“…The action that includes higher order interactions also has dimension 1 under the current scale transformation. However, we don't include them here as they do not give rise to IR singularities[54].…”

mentioning

confidence: 99%

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Fermi liquids beyond the forward scattering limit: the role of non-forward scatterings for scale invariance and instabilities

Ma¹,

Lee²

2023

Preprint

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Landau Fermi liquid theory is a fixed point theory of metals that includes the forward scattering amplitudes as exact marginal couplings. However, the fixed point theory that only includes the strict forward scatterings is non-local in real space. In this paper, we revisit the Fermi liquid theory using the field-theoretic functional renormalization group formalism and show how the scale invariant fixed point emerges as a local theory. The local low-energy effective field theory for Fermi liquids includes not only the forward scatterings but also non-forward scatterings with small but non-zero momentum transfers. In the low-energy limit, the non-forward scattering amplitude takes a scale invariant form if the momentum transfer is scaled along with the energy. If the bare coupling is attractive beyond a critical strength, the coupling function exhibits a run-away flow, signifying potential instabilities in particle-hole channels.What drives those instabilities is the non-trivial renormalization group flow of the non-forward scattering amplitudes. The pairing interaction also obeys a scaling relation if the center of mass momentum of Cooper pairs is comparable with energy.

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Review and History of Fermi Liquid Theory

Mehta

2024

Springer Theses

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

Cited by 12 publications

References 93 publications

Loop current fluctuations and quantum critical transport

Loop current fluctuations and quantum critical transport

Fermi liquids beyond the forward scattering limit: the role of non-forward scatterings for scale invariance and instabilities

Review and History of Fermi Liquid Theory

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