Item

Abstract

Expansion many-body methods correspond to solving complex tensor
networks. The (iterative) solving of the network and the (repeated)
storage of the unknown tensors requires a computing power growing
polynomially with the size of basis of the one-body Hilbert space one is
working with. Thanks to current computer capabilities, ab initio
calculations of nuclei up to mass A similar to 100 delivering a few
percent accuracy are routinely feasible today. However, the runtime and
memory costs become quickly prohibitive as one attempts (possibly at the
same time) (i) to reach out to heavier nuclei, (ii) to employ
symmetry-breaking reference states to access open-shell nuclei and (iii)
to aim for yet a greater accuracy. The challenge is particularly
exacerbated for non-perturbative methods involving the repeated storage
of (high-rank) tensors obtained via iterative solutions of nonlinear
equations. The present work addresses the formal and numerical
implementations of so-called importance truncation (IT) techniques
within the frame of one particular nonperturbative expansion method,
i.e., Gorkov Self-Consistent Green's Function (GSCGF) theory, with the
goal to eventually overcome above-mentioned limitations. By a priori
truncating irrelevant tensor entries, IT techniques are shown to reduce
the storage to less than 1% of its original cost in realistic GSCGF
calculations performed at the ADC(2) level while maintaining a 1%
accuracy on the correlation energy. The future steps will be to extend
the present development to the next, e.g., ADC(3), truncation level and
to SCGF calculations applicable to doubly open-shell nuclei.