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Numerical simulations based on electronic structure calculations are findingever growing applications in many areas of physics. A major limiting factor ishowever the cubic scaling of the algorithms used. Building on previous work [F.R. Krajewski and M. Parrinello, Phys.Rev. B71, 233105 (2005)] we introduce anovel statistical method for evaluating the inter-atomic forces which scaleslinearly with system size and is applicable also to metals. The method is basedon exact decomposition of the fermionic determinant and on a mapping onto afield theoretical expression. We solve exactly the problem of sampling theBoltzmann distribution with noisy forces. This novel approach can be used insuch diverse fields as quantum chromodynamics, quantum Monte Carlo or colloidalphysics.Comment: 5 pages, 2 figure

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