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 $delta\xi=Omega/sqrt{Lln(L)}$. 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.

### 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 $delta\xi=Omega/sqrt{Lln(L)}$. 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.
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Alba, Vincenzo
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/1142434
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