Ladder-like optical conductivity in the spin-fermion model

In the nested limit of the spin-fermion model for the cuprates, 1D-type physics in the form of half-filled two-leg ladders emerges. We show that the RG flow of the corresponding ladder is towards the dMott phase, a gapped spin-liquid with short-ranged d-wave pairing correlations, and reveals an intermediate SO(5)xSO(3) symmetry. We use the results of the RG 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 hotspot region dominate the transport. For finite temperature, we determine the resistivity in the zero-frequency limit. We argue that Umklapp processes play a major role. Our results show an approximate linear temperature dependence of the resistivity and a conductivity that follows a non-universal power law, qualitatively consistent with experiment.