  In this note, we consider entanglement and Renyi entropies for spatial
subsystems of a boundary conformal field theory (BCFT) or of a CFT in a state
constructed using a Euclidean BCFT path integral. Holographic calculations
suggest that these entropies undergo phase transitions as a function of time or
parameters describing the subsystem; these arise from a change in topology of
the RT surface. In recent applications to black hole physics, such transitions
have been seen to govern whether or not the bulk entanglement wedge of a (B)CFT
region includes a portion of the black hole interior and have played a crucial
role in understanding the semiclassical origin of the Page curve for
evaporating black holes.
  In this paper, we reproduce these holographic results via direct (B)CFT
calculations. Using the replica method, the entropies are related to
correlation functions of twist operators in a Euclidean BCFT. These
correlations functions can be expanded in various channels involving
intermediate bulk or boundary operators. Under certain sparseness conditions on
the spectrum and OPE coefficients of bulk and boundary operators, we show that
the twist correlators are dominated by the vacuum block in a single channel,
with the relevant channel depending on the position of the twists. These
transitions between channels lead to the holographically observed phase
transitions in entropies.
