Linear scaling electronic structure calculations and accurate statistical mechanics sampling with noisy forces

Numerical simulations based on electronic structure calculations are finding ever growing applications in many areas of physics. A major limiting factor, however, is the cubic scaling of the algorithms used. Building on previous work Phys. Rev. B 71, 233105 (2005) we introduce a statistical method for evaluating interatomic forces, which scales linearly with system size and is applicable also to metals. The method is based on exact decomposition of the fermionic determinant and on a mapping onto a field theoretical expression. We solve the problem of an accurate sampling of the Boltzmann distribution with noisy forces. This novel approach can be used in such diverse fields as quantum chromodynamics, quantum Monte Carlo, or colloidal physics.