  The search for a resonant four-neutron system has been revived thanks to the
recent experimental hints reported in Phys. Rev. Lett. \textbf{116}, 052501
(2016). The existence of such a system would deeply impact our understanding of
nuclear matter and requires a critical investigation. In this work, we study
the existence of a four-neutron resonance in the quasi-stationary formalism
using \textit{ab initio} techniques with various two-body chiral interactions.
We employ the No-Core Gamow Shell Model and the Density Matrix Renormalization
Group method, both supplemented by the use of natural orbitals and a new
identification technique for broad resonances. We demonstrate that while the
energy of the four-neutron system may be compatible with the experimental
value, its width must be larger than the reported upper limit, supporting the
interpretation of the experimental observation as a reaction process too short
to form a nucleus.
