Accueil du site > Publications récentes > Combining symmetry breaking and restoration with configuration interaction : A highly accurate many-body scheme applied to the pairing Hamiltonian
J. Ripoche, D. Lacroix, D. Gambacurta, J.-P. Ebran, and T. Duguet
Background : Ab initio many-body methods have been
developed over the past ten years to address mid-mass nuclei.
In their best current level of implementation, their accuracy
is of the order of a few percent error on the ground-state
correlation energy. Recently implemented variants of these
methods are operating a breakthrough in the description of
medium-mass open-shell nuclei at a polynomial computational
cost while putting state-of-the-art models of internucleon
interactions to the test.
Purpose : As progress in the design of internucleon
interactions is made, and as questions one wishes to answer
are refined in connection with increasingly available
experimental data, further efforts must be made to tailor
many-body methods that can reach an even higher precision for
an even larger number of observable quantum states or nuclei.
The objective of the present work is to contribute to such a
quest by designing and testing a new many-body scheme.
Methods : We formulate a truncated configuration-interaction
method that consists of diagonalizing the Hamiltonian in a
highly truncated subspace of the total N-body Hilbert space.
The reduced Hilbert space is generated via the particle-number
projected BCS state along with projected seniority-zero two-
and four-quasiparticle excitations. Furthermore, the extent by
which the underlying BCS state breaks U(1) symmetry is
optimized in the presence of the projected two- and
four-quasiparticle excitations. This constitutes an extension
of the so-called restricted variation after projection method
in use within the frame of multireference energy density
functional calculations. The quality of the newly designed
method is tested against exact solutions of the so-called
attractive pairing Hamiltonian problem.
Results : By construction, the method reproduces exact results
for N=2 and N=4. For N=(8,16,20), the error in the
ground-state correlation energy is less than (0.006%, 0.1%,
0.15%) across the entire range of internucleon coupling
defining the pairing Hamiltonian and driving the
normal-to-superfluid quantum phase transition. The presently
proposed method offers the advantage of automatic access to
the low-lying spectroscopy, which it does with high accuracy.
Conclusions : The numerical cost of the newly designed
variational method is polynomial (N6) in system size. This
method achieves unprecedented accuracy for the ground-state
correlation energy, effective pairing gap, and one-body
entropy as well as for the excitation energy of low-lying
states of the attractive pairing Hamiltonian. This constitutes
a sufficiently strong motivation to envision its application
to realistic nuclear Hamiltonians in view of providing a
complementary, accurate, and versatile ab initio description
of mid-mass open-shell nuclei in the future.
Voir en ligne : Phys. Rev. C.95.014326
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