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arXiv:1808.02756 · Physical review. B./Physical review. B

Non-Fermi-liquid fixed points and anomalous Landau damping in a quantum critical metal

M. Trott, C. Hooley

Published Nov 27, 2018• 5 citations
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Abstract

We present a functional renormalization-group calculation of the properties of a quantum critical metal in $d=2$ spatial dimensions. Our theory describes a general class of Pomeranchuk instabilities with ${N}_{b}$ flavors of boson. At small ${N}_{b}$ we find a family of fixed points characterized by weakly non-Fermi-liquid behavior of the conduction electrons and $z\ensuremath{\approx}2$ critical dynamics for the order-parameter fluctuations, in agreement with the scaling observed by Schattner et al. [Phys. Rev. X 6, 031028 (2016)] for the Ising-nematic transition. Contrary to recent suggestions that this represents an intermediate regime en route to the scaling limit, our calculation suggests that this behavior may persist all the way to the critical point. As the number of bosons ${N}_{b}$ is increased, the model's fixed-point properties cross over to $z\ensuremath{\approx}1$ scaling and non-Fermi-liquid behavior similar to that obtained by Fitzpatrick et al. [Phys. Rev. B 88, 125116 (2013)].

DOI
10.1103/physrevb.98.201113

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We study the problem of disorder-free metals near a continuous quantum critical point. We depart from the standard paradigm [Hertz, Phys. Rev. B 14, 1165 (1976) and Millis, Phys. Rev. B 48, 7183 (1993)] and treat both fermions and bosons (i.e., order parameter fields) on equal footing. We construct a Wilsonian effective field theory that integrates out only high-energy boson and fermion modes. Below the upper critical dimension of the theory (d=3d=3d=3 spatial dimensions), we find new fixed points in which the bosons are described by the Wilson-Fisher fixed point and are coupled to a non-Fermi-liquid metal. We describe subtleties with the renormalization group flow of four-Fermi interactions, which can be surmounted in a controlled large-NNN limit. In this limit, we find that the theory has no superconducting instability.
Understanding the influence of quenched random potential is crucial for comprehending the exotic electronic transport of non-Fermi liquid metals near metallic quantum critical points. In this study, we identify a stable fixed point governing the quantum critical behavior of two-dimensional non-Fermi liquid metals in the presence of a random potential disorder. By performing renormalization group analysis on a dimensional-regularized field theory for Ising-nematic quantum critical points, we systematically investigate the interplay between random potential disorder for electrons and Yukawa-type interactions between electrons and bosonic order-parameter fluctuations in a perturbative epsilon expansion. At the one-loop order, the effective field theory lacks stable fixed points, instead exhibiting a runaway flow toward infinite disorder strength. However, at the two-loop order, the effective field theory converges to a stable fixed point characterized by finite disorder strength, termed the “disordered non-Fermi liquid (DNFL) fixed point”. Our investigation reveals that two-loop vertex corrections induced by Yukawa couplings are pivotal in the emergence of the DNFL fixed point, primarily through screening disorder scattering. Additionally, the DNFL fixed point is distinguished by a substantial anomalous scaling dimension of fermion fields, resulting in pseudogap-like behavior in the electron’s density of states. These findings shed light on the quantum critical behavior of disordered non-Fermi liquid metals, emphasizing the indispensable role of higher-order loop corrections in such comprehension.
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The destruction of Fermi-liquid behavior when a gapless Fermi surface is coupled to a fluctuating gapless boson field is studied theoretically. This problem arises in a number of different contexts in quantum many-body physics. Examples include fermions coupled to a fluctuating transverse gauge field pertinent to quantum spin-liquid Mott insulators, and quantum critical metals near a Pomeranchuk transition. We develop a controlled theoretical approach to determine the low-energy physics. Our approach relies on combining an expansion in the inverse number (N)(N)(N) of fermion species with a further expansion in the parameter $ϵ={z}_{b}\ensuremath{-}2$, where zb{z}_{b}zb​ is the dynamical critical exponent of the boson field. We show how this limit allows a systematic calculation of the universal low-energy physics of these problems. The method is illustrated by studying spinon Fermi-surface spin liquids, and a quantum critical metal at a second-order electronic nematic phase transition. We calculate the low-energy single-particle spectra, and various interesting two-particle correlation functions. In some cases, deviations from the popular random-phase approximation results are found. Some of the same universal singularities are also calculated to leading nonvanishing order using a perturbative renormalization-group calculation at small NNN extending previous results of Nayak and Wilczek. Implications for quantum spin liquids and for Pomeranchuk transitions are discussed. For quantum critical metals at a nematic transition, we show that the tunneling density of states has a power-law suppression at low energies.