{
  "id": "1810.08419",
  "version": "v1",
  "published": "2018-10-19T09:31:33.000Z",
  "updated": "2018-10-19T09:31:33.000Z",
  "title": "Tensor-decomposition techniques for ab initio nuclear structure calculations. From chiral nuclear potentials to ground-state energies",
  "authors": [
    "Alexander Tichai",
    "Roman Schutski",
    "Gustavo E. Scuseria",
    "Thomas Duguet"
  ],
  "comment": "16 pages, 13 figures, 1 table",
  "categories": [
    "nucl-th",
    "physics.chem-ph",
    "physics.comp-ph"
  ],
  "abstract": "The impact of applying state-of-the-art tensor factorization techniques to modern nuclear Hamiltonians derived from chiral effective field theory is investigated. Subsequently, the error induced by the tensor decomposition of the input Hamiltonian on ground-state energies of closed-shell nuclei calculated via second-order many-body perturbation theory is benchmarked. With the aid of the factorized Hamiltonian, the second-order perturbative correction to ground-state energies is decomposed and the scaling properties of the underlying tensor network are discussed. The employed tensor formats are found to lead to an efficient data compression of two-body matrix elements of the nuclear Hamiltonian. In particular, the sophisticated \\emph{tensor hypercontraction} (THC) scheme yields low tensor ranks with respect to both harmonic-oscillator and Hartree-Fock single-particle bases. It is found that the tensor rank depends on the two-body total angular momentum $J$ for which one performs the decomposition, which is itself directly related to the sparsity the corresponding tensor. Furthermore, including normal-ordered two-body contributions originating from three-body interactions does not compromise the efficient data compression. Ultimately, the use of factorized matrix elements authorizes controlled approximations of the exact second-order ground-state energy corrections. In particular, a small enough error is obtained from low-rank factorizations in $^{4}$He, $^{16}$O and $^{40}$Ca.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-19T09:31:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ab initio nuclear structure calculations",
      "chiral nuclear potentials",
      "tensor-decomposition techniques",
      "second-order ground-state energy corrections",
      "state-of-the-art tensor factorization techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}