A primal-dual semidefinite programming algorithm tailored to the variational determination of the two-body density matrix
Strongly Correlated Electrons
2011-10-27 v1 Computational Physics
Abstract
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.
Cite
@article{arxiv.1012.2059,
title = {A primal-dual semidefinite programming algorithm tailored to the variational determination of the two-body density matrix},
author = {B. Verstichel and H. van Aggelen and D. Van Neck and P. Bultinck and S. De Baerdemacker},
journal= {arXiv preprint arXiv:1012.2059},
year = {2011}
}
Comments
24 pages, 5 figures, submitted to the Journal of Computational Physics