Ladderlike optical conductivity in the spin-fermion model

In the nested limit of the spin-fermion model for the cuprates,one-dimensional physics in the form of half-filled two-leg laddersemerges. We show that the renormalization group flow of thecorresponding ladder is towards the d-Mott phase, a gapped spin-liquidwith short-ranged d-wave pairing correlations, and reveals anintermediate SO(5 ) × SO(3) symmetry. We use the results of therenormalization group in combination with a memory-function approach tocalculate the optical conductivity of the spin-fermion model in thehigh-frequency regime, where processes within the hot spot regiondominate the transport. We argue that umklapp processes play a majorrole. For finite temperatures, we determine the resistivity in thezero-frequency (dc) limit. Our results show an approximate lineartemperature dependence of the resistivity and a conductivity thatfollows a nonuniversal power law. A comparison to experimental datasupports our assumption that the conductivity is dominated by theantinodal contribution above the pseudogap