Boundary-corner entanglement for free bosons

Abstract

In quantum field theories defined on a spacetime with boundaries, the entanglement entropy exhibits subleading, boundary-induced corrections to the ubiquitous area law. At critical points described by conformal field theories (CFTs), and when the entangling surface intersects the physical boundary of the space, new universal terms appear in the entropy and encode valuable information about the boundary CFT. In $2+1$ dimensions, the universal subleading boundary term is logarithmic with coefficient $b(\theta )$ depending on the angle $\theta$ at which the entangling surface intersects the boundary, as well as on the boundary conditions (BCs). In this paper, we conduct a numerical study of $b(\theta )$ for free bosons on finite-size square lattices. We find a surprisingly accurate fit between our lattice results and the corresponding holographic function available in the literature. We also comment on the ratio $b^{\prime \prime }(\pi /2)/A_T$, where $A_T$ is the central charge in the near boundary expansion of the stress tensor, for which a holographic analysis suggests that it may be a universal quantity. Though we show evidence that this ratio is violated for the free boson with Dirichlet BCs, we conjecture its validity for free bosons evenly split between Dirichlet and Neumann BCs.

arXiv comment12 pages, 8 figures; v2: typos corrected, matches published version

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