  Simulations in the warm dense matter regime using finite temperature
Kohn-Sham density functional theory (FT-KS-DFT), while frequently used, are
computationally expensive due to the partial occupation of a very large number
of high-energy KS eigenstates which are obtained from subspace diagonalization.
We have developed a stochastic method for applying FT-KS-DFT, that overcomes
the bottleneck of calculating the occupied KS orbitals by directly obtaining
the density from the KS Hamiltonian. The proposed algorithm, scales as
$O\left(NT^{-1}\right)$ and is compared with the high-temperature limit scaling
$O\left(N^{3}T^{3}\right)$ of the deterministic approach, where $N$ is the
system size (number of electrons, volume etc.) and $T$ is the temperature. The
method has been implemented in a plane-waves code within the local density
approximation (LDA); we demonstrate its efficiency, statistical errors and bias
in the estimation of the free energy per electron for a diamond structure
silicon. The bias is small compared to the fluctuations, and is independent of
system size. In addition to calculating the free energy itself, one can also
use the method to calculate its derivatives and obtain the equations of state.
