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
Computer Physics Communications
182 (6), 1235-1244


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.
Keywords: Density matrix; Variational; Semidefinite programming

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