  We construct a fully quantum zero-temperature electron star in a soft-wall
regulated anti-de-Sitter Einstein-Maxwell-Dirac theory that is
thermodynamically stable compared to the Reissner-Nordstr\"{o}m black hole. The
soft wall only acts on the effective mass of the fermionic degrees of freedom,
and allows for a controlled fully backreacted solution. The star is
holographically dual to an RG flow where a gapped Fermi liquid starts to emerge
from a UV CFT, but decouples again once the effective energy scale becomes
lower than the the gap of the fermionic degrees of freedom. The RG flow then
returns to a non-trivial strongly coupled relativistic fixed point with a
holographic dual. Our regulated quantum electron star is thus the fermionic
analogue of the Horowitz-Roberts-Gubser-Rocha AdS-to-AdS domain wall solution
for the holographic superconductor.
