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We study the conductivity from higher derivative electrodynamics in aholographic quantum critical phase (QCP). Two key features of this model areobserved. First, a rescaling for the Euclidean frequency by a constant isneeded when fitting the quantum Monte Carlo (QMC) data for the $O(2)$ QCP. Weconclude that it is a common characteristic of the higher derivativeelectrodynamics. Second, both the Drude-like peak at low frequency and thepronounced peak can simultaneously emerge. They are more evident for therelevant operators than for the irrelevant operators. In addition, our resultalso further confirms that the conductivity for the $O(2)$ QCP is particle-likebut not vortex-like. Finally, the electromagnetic (EM) duality is brieflydiscussed. The largest discrepancies of the particle-vortex duality in theboundary theory appear at the low frequency and the particle-vortex dualityholds more well for the irrelevant operator than for the relevant operator.

Holographic quantum critical conductivity from higher derivative electrodynamics