Efficient computation of Hamiltonian matrix elements between non-orthogonal Slater determinants

Abstract

We present an efficient numerical method for computing Hamiltonian matrix elements between non-orthogonal Slater determinants, focusing on the most time-consuming component of the calculation that involves a sparse array. In the usual case where many matrix elements should be calculated, this computation can be transformed into a multiplication of dense matrices. It is demonstrated that the present method based on the matrix-matrix multiplication attains $\sim$80% of the theoretical peak performance measured on systems equipped with modern microprocessors, a factor of 5-10 better than the normal method using indirectly indexed arrays to treat a sparse array. The reason for such different performances is discussed from the viewpoint of memory access.

8 pages, 3 figures

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• Projected Quasiparticle Theory for Molecular Electronic Structure
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• Efficient computation of matrix elements of generic Slater determinants
• New Generation of the Monte Carlo Shell Model for the K Computer Era
• Exact solutions of the nuclear shell-model secular problem: Discrete Non-Orthogonal Shell Model within a Variation After Projection approach
• Precise Quantum Chemistry calculations with few Slater Determinants