Conductivity between Luttinger liquids: coupled chains and bilayer graphene

The conductivity properties between Luttinger liquids are analyzed by exact renormalization-group methods. We prove that in a two chain system or in a model of bilayer graphene, described by two coupled Fermionic honeycomb lattices interacting with a gauge field, the transverse optical conductivity at finite temperature is anomalous and decreasing together with the frequency as a power law with a Luttinger liquid exponent.