Entanglement gap, corners, and symmetry breaking

Abstract

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

21 pages, 5 figures. arXiv admin note: text overlap with arXiv:2009.04235. Typos corrected, minor modifications