I have been trying to understand the Drude Weight quantity that is used in the Metal-Insulator transition and Spin chain literature, and I have not been able to find any clear intuitive explanations of what it means, where it comes from and when it is useful.
It is usually defined as part of the frequency-dependent conductivity:
$$
\sigma(\omega) = 2 \pi \, D \, \delta(\omega) + \sigma_{\textrm{reg}}(\omega)
$$
where $D$ is the Drude weight and $\sigma_{\textrm{reg}}$ is a regular function of $\omega$. This seems like the Drude weight is just the $\omega = 0$ component of the conductivity, i.e. the D.C. conductivity, is that true and if not how are the two different?
Best Answer
just a comment on your answer: Drude weight is not charactering the superconducting, it is only used to distinguish metal and insulator. The constant value simply because there is no dissipation in Drude theory. You can refer to the paper by PRB 47, 7995 (1993).