Ladder-like 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 ladders emerges. We show that the renormalization group flow of the corresponding ladder is towards the d-Mott phase, a gapped spin-liquid with short-ranged d-wave pairing correlations, and reveals an intermediate SO(5)$\times$SO(3) symmetry. We use the results of the renormalization group in combination with a memory-function approach to calculate the optical conductivity of the spin-fermion model in the high-frequency regime, where processes within the hot spot region dominate the transport. We argue that umklapp processes play a major role. For finite temperatures, we determine the resistivity in the zero-frequency (dc) limit. Our results show an approximate linear temperature dependence of the resistivity and a conductivity that follows a non-universal power law. A comparison to experimental data supports our assumption that the conductivity is dominated by the antinodal contribution above the pseudogap.