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...

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Bibliographic Details
Published inComputer physics communications Vol. 182; no. 6; pp. 1235 - 1244
Main Authors Verstichel, Brecht, van Aggelen, Helen, Van Neck, Dimitri, Bultinck, Patrick, De Baerdemacker, Stijn
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2011
Subjects
Density matrix
Semidefinite programming
Variational
Density matrix
Variational
Semidefinite programming
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ISSN0010-4655
1879-2944
DOI10.1016/j.cpc.2011.02.005

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Summary: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.
ISSN:0010-4655
1879-2944
DOI:10.1016/j.cpc.2011.02.005