  In this paper, we study the bulk entanglement entropy evolution in conical
BTZ black bole background using the heat kernel method. This is motivated by
exploring the new examples where quantum corrections of entanglement entropy
give the leading contribution. We find that in the large black hole limit the
bulk entanglement entropy decreases under the double-trace deformation which is
consistent with the holographic $c$ theorem and in the small black hole limit
the bulk entanglement entropy increases under the double-trace deformation.
