Non-linear, Finite Frequency Quantum Critical Transport from AdS/CFT

TL;DR

This paper uses holographic duality to analyze the nonlinear and finite-frequency electrical transport properties at quantum critical points, revealing instantaneous responses and frequency-independent conductivities in certain models.

Contribution

It provides a comprehensive calculation of nonlinear, finite-frequency conductivity at quantum critical points using gauge/gravity duality, including time-dependent responses in 2+1 dimensions.

Findings

Conductivity is frequency independent in certain models.

System exhibits instantaneous response to electric fields.

Full nonlinear and finite-frequency transport behavior characterized.

Abstract

Transport at a quantum critical point depends sensitively on the relative magnitudes of temperature, frequency and electric field. Here we used the gauge/gravity correspondence to compute the full temperature and, generally nonlinear, electric field dependence of the electrical conductivity for some model critical theories. In the special case of 2+1 dimensions we are also able to find the full time-dependent response of the system to an arbitrary time dependent external electric field. The response of the system is instantaneous, implying a frequency independent conductivity. We describe a mechanism that rationalizes the instantaneous response.