Temperature dependence of optical spectral weights in quarter-filled ladder systems

The temperature dependence of the integrated optical conductivity I(T) reflects the changes of the kinetic energy as spin and charge correlations develop. It provides a unique way to explore experimentally the kinetic properties of strongly correlated systems. We calculated I(T) in the frame of a t-J-V model at quarter-filling for ladder systems, like NaV_2O_5, and show that the measured strong T dependence of I(T) for NaV_2O_5 can be explained by the destruction of short range antiferromagnetic correlations. Thus I(T) provides detailed information about super-exchange and magnetic energy scales.