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We consider the entanglement entropy in critical one-dimensional quantumsystems with open boundary conditions. We show that the second R\'enyi entropyof an interval away from the boundary can be computed exactly, provided thesame conformal boundary condition is applied on both sides. The result involvesthe annulus partition function. We compare our exact result with numericalcomputations for the critical quantum Ising chain with open boundaryconditions. We find excellent agreement, and we analyse in detail thefinite-size corrections, which are known to be much larger than for a periodicsystem.

Second R\'enyi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries