Corrections to scaling in entanglement entropy from boundary perturbations

Abstract: We investigate the corrections to scaling of the Renyi entropies of a region of size l at the end of a semi-infinite one-dimensional system described by a conformal field theory when the corrections come from irrelevant boundary operators. The corrections from irrelevant bulk operators with scaling dimension x have been studied by Cardy and Calabrese (2010), and they found not only the expected corrections of the form l^4-2x but also unusual corrections that could not have been anticipated by finite-size scaling arguments alone. However, for the case of perturbations from irrelevant boundary operators we find that the only corrections that can occur to leading order are of the form l^2-2x_b for boundary operators with scaling dimension x_b < 3/2, and l^-1 when x_b > 3/2. When x_b=3/2 they are of the form l^-1log(l). A marginally irrelevant boundary perturbation will give leading corrections going as log(l)^-3. No unusual corrections occur when perturbing with a boundary operator.