Linear scaling electronic structure Monte Carlo method for metals

We present a method for sampling the Boltzmann distribution of a system in which the interionic interactions are derived from empirical or semiempirical electronic structure calculations within the Born-Oppenheimer approximation. We considerably improve on a scheme presented earlier [F. R. Krajewski and M. Parrinello, Phys. Rev. B 73, 041105(R) (2006)]. To this effect, we use an expression for the partition function in which electronic and ionic degrees of freedom are treated on the same footing. In addition, we introduce an auxiliary set of fields in such a way that the sampling of the partition function scales linearly with system size. We demonstrate the validity of this approach on tight-binding models of carbon nanotubes and silicon in its liquid and crystalline phases.