Diagrammatic study of optical excitations in correlated systems
Olivier Simard, Shintaro Takayoshi, Philipp Werner
Abstract
The optical conductivity contains relevant information on the properties of correlated electron systems. In infinite dimensions, where dynamical mean field theory becomes exact, vertex corrections can be neglected and the conductivity computed from particle-hole bubbles. An interesting question concerns the nature and effect of the most relevant vertex corrections in finite-dimensional systems. A recent numerical study showed that the dominant vertex correction near an ordering instability with wave vector $\ensuremath{\pi}$ comes from a vertical ladder, analogous to the Maki-Thompson diagram. Since the random phase approximation version of this ladder diagram, dubbed $\ensuremath{\pi}$-ton, can be easily evaluated, this suggests a simple procedure for incorporating antiferromagnetic or charge density wave fluctuations into dynamical mean field estimates of the optical conductivity and related susceptibilities. We implement this procedure for the half-filled Hubbard model, considering the $\ensuremath{\pi}$-ton, a double-ladder extension of the $\ensuremath{\pi}$-ton and Aslamazov-Larkin-type diagrams, and reveal the spectral signatures of these vertex corrections.