322 research outputs found
An efficient and accurate decomposition of the Fermi operator
We present a method to compute the Fermi function of the Hamiltonian for a
system of independent fermions, based on an exact decomposition of the
grand-canonical potential. This scheme does not rely on the localization of the
orbitals and is insensitive to ill-conditioned Hamiltonians. It lends itself
naturally to linear scaling, as soon as the sparsity of the system's density
matrix is exploited. By using a combination of polynomial expansion and
Newton-like iterative techniques, an arbitrarily large number of terms can be
employed in the expansion, overcoming some of the difficulties encountered in
previous papers. Moreover, this hybrid approach allows us to obtain a very
favorable scaling of the computational cost with increasing inverse
temperature, which makes the method competitive with other Fermi operator
expansion techniques. After performing an in-depth theoretical analysis of
computational cost and accuracy, we test our approach on the DFT Hamiltonian
for the metallic phase of the LiAl alloy.Comment: 8 pages, 7 figure
A hybrid approach to Fermi operator expansion
In a recent paper we have suggested that the finite temperature density
matrix can be computed efficiently by a combination of polynomial expansion and
iterative inversion techniques. We present here significant improvements over
this scheme. The original complex-valued formalism is turned into a purely real
one. In addition, we use Chebyshev polynomials expansion and fast summation
techniques. This drastically reduces the scaling of the algorithm with the
width of the Hamiltonian spectrum, which is now of the order of the cubic root
of such parameter. This makes our method very competitive for applications to
ab-initio simulations, when high energy resolution is required.Comment: preprint of ICCMSE08 proceeding
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