48,588 research outputs found
A primal-dual semidefinite programming algorithm tailored to the variational determination of the two-body density matrix
The quantum many-body problem can be rephrased as a variational determination
of the two-body reduced density matrix, subject to a set of N-representability
constraints. The mathematical problem has the form of a semidefinite program.
We adapt a standard primal-dual interior point algorithm in order to exploit
the specific structure of the physical problem. In particular the matrix-vector
product can be calculated very efficiently. We have applied the proposed
algorithm to a pairing-type Hamiltonian and studied the computational aspects
of the method. The standard N-representability conditions perform very well for
this problem.Comment: 24 pages, 5 figures, submitted to the Journal of Computational
Physic
Parallel eigensolvers in plane-wave Density Functional Theory
We consider the problem of parallelizing electronic structure computations in
plane-wave Density Functional Theory. Because of the limited scalability of
Fourier transforms, parallelism has to be found at the eigensolver level. We
show how a recently proposed algorithm based on Chebyshev polynomials can scale
into the tens of thousands of processors, outperforming block conjugate
gradient algorithms for large computations
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