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arXiv · 1012.2059

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

B. Verstichel·H. van Aggelen·D. Van Neck·P. Bultinck·S. De Baerdemacker
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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.

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B. Verstichel, H. van Aggelen, D. Van Neck, P. Bultinck, S. De Baerdemacker. 2010-12-09. A primal-dual semidefinite programming algorithm tailored to the variational determination of the two-body density matrix. https://doi.org/10.1016/j.cpc.2011.02.005

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