Loop current fluctuations and quantum critical transport

Abstract

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.

Universal theory of strange metals from spatially random interactions

“…The mechanism in the work of Shi et al . ( 22 ) for the noncommutativity of the large N and small ω limits applies only for order parameters with the same symmetry as the momentum in the spatially uniform case and does not apply for the spatially disordered case, which has no conserved momentum and for which the patches do not decouple.…”

“…The large N computation of the conductivity ( 17 , 22 ) yields only the clean Drude result Reσω/N=πNvF2δω/2, where N=m/2π is the fermion density of states at the Fermi level. This is in contrast to the results of previous studies ( 12 , 40 ), in which it has been found that dc resistivity is ~ T 4/3 and optical conductivity is ∼ω−2/3.…”

“…However, despite these advances, theory has so far found limited success in explaining all of the defining transport properties (such as the linear-in- T resistivity) of strange metals. Conservation of momentum in the low-energy theory of a clean metal implies that the dc and optical conductivities are not affected by the anomalous self-energy of the excitations near the Fermi surface ( 15 – 17 , 19 – 22 ). In other words, the strong coupling between the Fermi surface and the scalar field places the system in the limit of strong scalar drag, and this clean metal theory cannot describe strange metal behavior.…”

A criterion for strange metallicity in the Lorenz ratio

“…An intriguing issue concerns the application of our criterion to theories of quantum-critical metals, especially in cases where the electrical resistivity is T − linear 27 , 61 , 62 . In this regard, we point out ref.…”