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

The temperature dependence of the integrated optical conductivity $I\left(T\right)\mathrm{}$ reflects the changes of the kinetic energy as spin and charge correlations develop. We calculated $I\left(T\right)\mathrm{}$ in the frame of a $t-J-V$ model for ladder systems, such as ${\alpha }^{\prime }-{\mathrm{NaV}}_2{\mathrm{O}}_5,$ and show that the measured strong T dependence of $I\left(T\right)\mathrm{}$ for ${\mathrm{NaV}}_2{\mathrm{O}}_5$ can be explained by the destruction of short-range antiferromagnetic correlations. Thus $I\left(T\right)\mathrm{}$ provides detailed information about the T dependence of superexchange energy and thereby allows for an independent determination of magnetic energy scales.