Entanglement gap, corners, and symmetry breaking

TL;DR

This paper studies how the entanglement gap scales with system size in the 2D quantum spherical model, revealing different decay behaviors in ordered and critical phases and analyzing the impact of corners and symmetry breaking.

Contribution

It provides an analytical derivation of the entanglement gap scaling and its dependence on geometry and low-energy dispersion in the 2D quantum spherical model.

Findings

Entanglement gap decays as $rac{ ext{constant}}{\sqrt{L\ln(L)}}$ in the ordered phase.

At the critical point, the decay is purely logarithmic, $rac{ ext{constant}}{\ln(L)}$.

Corner contributions to the entanglement gap are explicitly computed for square corners.

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.