Incoherent transport in clean quantum critical metals

TL;DR

The work identifies an intrinsic, incoherent conductivity σ_Q in clean quantum critical metals at finite density, arising from a current that decouples from momentum. It establishes that σ_Q governs diffusive transport via D = σ_Q/χ^{inc} and can be computed holographically through horizon data, with a general horizon formula σ_Q = Z_+(a_x^{(0)}(r_+))^2 and a concrete massless-photon result σ_Q = Z_+ (s T/(ε+P))^2. A scaling framework with exponents z, θ, and Φ predicts σ_Q ∼ T^{(d-2-θ+2Φ)/z}, and in the marginal-density regime (Φ = z) reproduces the characteristic holographic σ_Q ∼ T^2 in two spatial dimensions, linking IR criticality to universal transport. The results unify holographic and scaling perspectives on incoherent diffusion, clarify distinctions from other conductivities, and point toward bounds and applications in compressible quantum critical phases.

Abstract

In a clean quantum critical metal, and in the absence of umklapp, most d.c. conductivities are formally infinite due to momentum conservation. However, there is a particular combination of the charge and heat currents which has a finite, universal conductivity. In this paper, we describe the physics of this conductivity $σ_Q$ in quantum critical metals obtained by charge doping a strongly interacting conformal field theory. We show that it satisfies an Einstein relation and controls the diffusivity of a conserved charge in the metal. We compute $σ_Q$ in a class of theories with holographic gravitational duals. Finally, we show how the temperature scaling of $σ_Q$ depends on certain critical exponents characterizing the quantum critical metal. The holographic results are found to be reproduced by the scaling analysis, with the charge density operator becoming marginal in the emergent low energy quantum critical theory.