  Ab initio many-body methods address closed-shell nuclei up to mass A ~ 130 on
the basis of realistic two- and three-nucleon interactions. Several routes to
address open-shell nuclei are currently under investigation, including ideas
which exploit spontaneous symmetry breaking. Singly open-shell nuclei can be
efficiently described via the sole breaking of $U(1)$ gauge symmetry associated
with particle number conservation, to account for their superfluid character.
The present work formulates and applies Bogoliubov coupled cluster (BCC)
theory, which consists of representing the exact ground-state wavefunction of
the system as the exponential of a quasiparticle excitation cluster operator
acting on a Bogoliubov reference state. Equations for the ground-state energy
and cluster amplitudes are derived at the singles and doubles level (BCCSD)
both algebraically and diagrammatically. The formalism includes three-nucleon
forces at the normal-ordered two-body level. The first BCC code is implemented
in $m$-scheme, which will eventually permit the treatment of doubly open-shell
nuclei. Proof-of-principle calculations in an $N_{\text{max}}=6$ spherical
harmonic oscillator basis are performed for $^{16,18,20}$O, $^{18}$Ne,
$^{20}$Mg in the BCCD approximation with a chiral two-nucleon interaction,
comparing to results obtained in standard coupled cluster theory when
applicable. The breaking of $U(1)$ symmetry is monitored by computing the
variance associated with the particle-number operator. The newly developed
many-body formalism increases the potential span of ab initio calculations
based on single-reference coupled cluster techniques tremendously, i.e.
potentially to reach several hundred additional mid-mass nuclei. The new
formalism offers a wealth of potential applications and further extensions
dedicated to the description of ground and excited states of open-shell nuclei.
