Title: Combining symmetry breaking and restoration with configuration interaction: extension to z-signature symmetry in the case of the Lipkin Model,
Abstract: Background: Ab initio many-body methods whose numerical cost scales
polynomially with the number of particles have been developed over the past
fifteen years to tackle closed-shell mid-mass nuclei. Open-shell nuclei have
been further addressed by implementing variants based on the concept of
spontaneous symmetry breaking (and restoration).
Purpose: In order to access the spectroscopy of open-shell nuclei more
systematically while controlling the numerical cost, we design a novel
many-body method that combines the merit of breaking and restoring symmetries
with those brought about by low-rank individual excitations.
Methods: The recently proposed truncated configuration-interaction method
based on optimized symmetry-broken and -restored states is extended to the
z-signature symmetry associated with a discrete subgroup of SU(2). The
highly-truncated N-body Hilbert subspace within which the Hamiltonian is
diagonalized is spanned by a z-signature broken and restored Slater determinant
vacuum and associated low-rank excitations.
Results: The proposed method provides an excellent reproduction of the
ground-state energy and of low-lying excitation energies of various
z-signatures and total angular momenta. In doing so, the successive benefits of
(i) breaking the symmetry, (ii) restoring the symmetry, (iii) including
low-rank particle-hole excitations and (iv) optimizing the amount by which the
underlying vacuum breaks the symmetry are illustrated.
Conclusions: The numerical cost of the newly designed variational method is
polynomial with respect to the system size. The present study confirms the
results obtained previously for the attractive pairing Hamiltonian in
connection with the breaking and restoration of U(1) global gauge symmetry.
These two studies constitute a strong motivation to apply this method to
realistic nuclear Hamiltonians.