Entanglement gap, corners, and symmetry breaking

We investigate the finite-size scaling of the lowest entanglement gap $δξ$ in the ordered phase of the two-dimensional quantum spherical model (QSM). The entanglement gap decays as $δξ=Ω/\sqrt{L\ln(L)}$. This is in contrast with the purely logarithmic behaviour as $δξ=π^2/\ln(L)$ at the critical point. The faster decay in the ordered phase reflects the presence of magnetic order. We analytically determine the constant $Ω$, 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 $Ω$, at least for the case of a square corner.

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