Optical Conductivity of the Two Dimensional Anti-ferromagnetic Quantum Critical Metal

In the two-dimensional anti-ferromagnetic quantum critical metal, coherent quasi-particle(s) ceases to exist at the hot spots due to strong coupling with soft spin fluctuations. Over an intermediate energy scale, physical responses of the non-Fermi liquid is controlled by the nesting angle between patches of Fermi surface connected by the anti-ferromagnetic wave-vector. For instance, the anomalous dimension of electron(s) at the hot spots defined over an intermediate energy scale decreases with decreasing nesting angle due to an increased damping of spin fluctuations by particle-hole excitation. In this work, we compute the optical conductivity of the non-Fermi liquid state as a function of the nesting angle. Remarkably, the weight of the conductivity that scales anomalously with frequency due to the soft spin fluctuations is enhanced as the nesting angle decreases. This is attributed to the fact that the increased number of electrons that are subject to scattering with spin fluctuations overcompensates the decreased scattering rate of individual electrons.