Normal-ordered k-body approximation in particle-number-breaking theories

Abstract

The reach of ab initio many-body theories is rapidly extending over the nuclear chart. However, dealing fully with three-nucleon, possibly four-nucleon, interactions makes the solving of the A-body Schrödinger equation particularly cumbersome, if not impossible beyond a certain nuclear mass. Consequently, ab initio calculations of mid-mass nuclei are typically performed on the basis of the so-called normal-ordered two-body (NO2B) approximation that captures dominant effects of three-nucleon forces while effectively working with twonucleon operators. A powerful idea currently employed to extend ab initio calculations to open-shell nuclei consists of expanding the exact solution of the A-body Schrödinger equation while authorizing the approximate solution to break symmetries of the Hamiltonian. In this context, operators are normal ordered with respect to a symmetry-breaking reference state such that proceeding to a naive truncation may lead to symmetry-breaking approximate operators. The purpose of the present work is to design a normal-ordering approximation of operators that is consistent with the symmetries of the Hamiltonian while working in the context of symmetry broken (and potentially restored) methods. Focusing on many-J. Ripoche CEA, DAM,

ADG: Automated generation and evaluation of many-body diagrams I. Bogoliubov many-body perturbation theory

“…[18] for terms up to O [4] and in Ref. [19] for O [6] . Each term O ij is characterized by its number i (j) of quasi-particle creation (annihilation) operators.…”

“…More details and properties can be found in Refs. [9,18,19]. State-of-the-art many-body calculations are typically performed within the normal-ordered two-body (NO2B) approximation [20][21][22][23].…”

“…The easiest way to install 19 ADG is to obtain it from the Python Package Index 20 by entering the following command pip3 install adg Provided setuptools is already installed, pip takes care of downloading and installing ADG as well as NumPy, SciPy and NetworkX. Once a new version of ADG is released, one can install it by entering the command pip3 install --upgrade adg 17 A valid partitioning relates to splitting the complete order p in a sum of terms that are individually proportional to a fraction of the form 1/(ǫ k i ...k j .…”

A Guided Tour of ab initio Nuclear Many-Body Theory

“…Thus, MBPT works best for ground states in systems with a strong energy gap, i.e., closed-shell nuclei, although extensions for more complex scenarios exist (see references [63, 68, 69] and references therein). A noteworthy new development is Bogoliubov MBPT, in which particle number symmetry is broken and eventually restored [77,80,81].…”

Self-Consistent Green's Function Theory for Atomic Nuclei

“…That is, using a different truncation than the e 3max truncation 21. It consists of two steps: (i) a normal ordering of the (3N) Hamiltonian with respect to a reference state and (ii) the disregard of operators of rank higher than two (see[146] for a pedagogical description and the generalization to the case of symmetry-breaking reference states).Frontiers in Physics | www.frontiersin.org…”