Electronic correlation effects influence the transport properties of solids profoundly. Many transition metal oxides, for example, are conductors according to band theory but insulators in reality, because of the strong correlation of the d electrons. Doped fullerenes are less strongly correlated, but their low-frequency optical conductivities nevertheless differ by an order of magnitude from those calculated using an independent electron model with the appropriate band masses [1]. The effects of correlation on electron transport are among the most studied but least understood phenomena in electronic structure and quantum many-body theory.

One of the main theoretical difficulties sounds almost trivial: how can you tell if a material is an insulator or a metal? An experimentalist might answer the question by observing the behaviour of the conductivity as the temperature is reduced. The most common theoretical approach is to look for a band gap. However, although the existence of a band gap is sufficient to guarantee insulating behaviour, it is not necessary, as shown by the example a non-interacting disordered solid in which the Fermi energy lies in a region of the band where all the states are Anderson localised. A more precise answer, which is also more closely related to experiment, was first given by Kohn [2]: in an ideal metal (in the absence of impurity scattering), the imaginary part of the zero-temperature optical conductivity o(w) diverges like 1/w as w tends to zero, while in an insulator it does not. Kohn also showed that w o''(w) (in the limit that w goes to zero), the quantity that characterises the metallic or insulating behaviour, is related to the change in the total energy of a finite periodic system as the boundary conditions are ``twisted''.

Kohn's prescription for obtaining the zero-frequency conductivity has been used in model calculations [3], but has never before been applied to a realistic solid. We believe, however, that it can be applied within QMC simulations. We therefore propose carrying out the first QMC calculations of the zero-frequency conductivities and Drude weights of several simple solids, including aluminium and carbon.