Entanglement gap, corners, and symmetry breaking

Abstract

We investigate the finite-size scaling of the lowest entanglement gap \delta\xiδξ in the ordered phase of the two-dimensional quantum spherical model (QSM). The entanglement gap decays as \delta\xi=\Omega/\sqrt{L\ln(L)}δξ=Ω/Lln(L). This is in contrast with the purely logarithmic behaviour as \delta\xi=\pi^2/\ln(L)δξ=π2/ln(L) at the critical point. The faster decay in the ordered phase reflects the presence of magnetic order. We analytically determine the constant \OmegaΩ, which depends on the low-energy part of the model dispersion and on the geometry of the bipartition. In particular, we are able to compute the corner contribution to \OmegaΩ, at least for the case of a square corner.