A primal-dual semidefinite programming algorithm tailored to the variational determination of the two-body density matrix

Physics – Condensed Matter – Strongly Correlated Electrons

Scientific paper

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24 pages, 5 figures, submitted to the Journal of Computational Physics

Scientific paper

10.1016/j.cpc.2011.02.005

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.

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