  Resonance is a general phenomenon which can happen in classic or quantum
systems. An unbound many-body quantum system can undergo a self-resonant
process. It has long been a challenge how to describe unbound many-body quantum
systems in resonances. In this paper, we develop a novel first-principles
method that is capable of describing resonant quantum systems. We exploit, for
the first time, the advanced in-medium similarity renormalization group (IMSRG)
in the complex-energy Gamow-Berggren representation with resonance and
non-resonant continuum. The ab initio Gamow IMSRG has broad applications, such
as, to the electromagnetic-interaction systems of atoms, molecules or quantum
dots, and strong-interaction atomic nuclei. In the present work, we apply the
method to loosely bound or unbound nuclear systems. Carbon and oxygen isotopes
have been investigated with an optimized chiral effective field theory
potential. The resonant states observed in neutron-rich 22O and 24O are well
reproduced. The loose halo structure of the Borromean nucleus 22C is clearly
seen by the density calculation, in which the continuum s-waves play a crucial
role. Further, we predict low-lying resonant excited states in 22C. This method
provides rigorous and tractable theoretical calculations for weakly-bound or
unbound open quantum systems.
