Diagrammatic study of optical excitations in correlated systems

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 computed from particle-hole bubbles. An interesting question concerns nature effect most in finite-dimensional A recent numerical study showed that dominant correction near an ordering instability with wave vector $\ensuremath{\pi}$ comes a vertical ladder, analogous to Maki-Thompson diagram. Since random phase approximation version this ladder diagram, dubbed $\ensuremath{\pi}$-ton, easily evaluated, suggests simple procedure for incorporating antiferromagnetic or charge density fluctuations into estimates related susceptibilities. We implement half-filled Hubbard model, considering double-ladder extension $\ensuremath{\pi}$-ton Aslamazov-Larkin-type diagrams, reveal spectral signatures these corrections.