Physics at the entangling surface

To consider the entanglement between the spatial region A and its complement in a QFT, we need to assign a Hilbert space $H_A$ to the region. Usually, some boundary condition on ∂A is implicitly chosen, but we argue that the choice of the boundary condition at ∂A is physically meaningful and affects the subleading contributions to the entanglement Rényi entropy. We investigate these issues in the context of 2d CFTs, and show that we can indeed read off the Cardy states of the c = 1/2 minimal model from the entanglement entropy of the critical Ising chain. (paper)