  In the AdS$_3$/CFT$_2$ correspondence, we find some conformal field theory
(CFT) states that have no bulk description by the Ba\~nados geometry. We
elaborate the constraints for a CFT state to be geometric, i.e., having a dual
Ba\~nados metric, by comparing the order of central charge of the
entanglement/R\'enyi entropy obtained respectively from the holographic method
and the replica trick in CFT. We find that the geometric CFT states fulfill
Bohr's correspondence principle by reducing the quantum KdV hierarchy to its
classical counterpart. We call the CFT states that satisfy the geometric
constraints geometric states, and otherwise non-geometric states. We give
examples of both the geometric and non-geometric states, with the latter case
including the superposition states and descendant states.
