  We show that $3$-dimensional AdS spacetime can be semiclassically unstable
due to strongly interacting quantum field effects. In our previous paper, we
have pointed out the possibility of such an instability of AdS$_3$ by
inspecting linear perturbations of the (covering space of) static BTZ black
hole with AdS${}_4$ gravity dual in the context of holographic semiclassical
problems. In the present paper, we further study this issue from thermodynamic
viewpoint by constructing asymptotically AdS$_3$ semiclassical solutions and
computing free energies of the solutions. We find two asymptotically AdS${}_3$
solutions to the semiclassical Einstein equations with non-vanishing source
term: the one whose free energy is smaller than that of the BTZ with vanishing
source term and the other whose free energy is smaller than that of the global
AdS$_3$ with no horizon (thus manifestly zero-temperature background). The
instability found in this paper implies the breakdown of the maximal symmetries
of AdS$_3$, and its origin is different from the well-known semiclassical
linear instability since our holographic semiclassical Einstein equations in
$3$-dimensions do not involve higher order derivative terms.
