Corrections to scaling in entanglement entropy from boundary perturbations

TL;DR

This paper analyzes how irrelevant boundary operators affect the scaling corrections of entanglement entropy in one-dimensional conformal field theories, revealing specific correction forms depending on operator scaling dimensions.

Contribution

It provides a detailed characterization of boundary-induced correction terms to entanglement entropy, showing they differ from bulk operator corrections and depend on boundary operator dimensions.

Findings

Boundary corrections are of the form l^(2-2x_b) for x_b<3/2

Corrections are l^(-1) for x_b>3/2

Logarithmic corrections occur at x_b=3/2

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^(-1)log(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.