Entanglement gap in 1D long-range quantum spherical models

We investigate the finite-size scaling of the entanglement gap in the onedimensional long-range quantum spherical model (QSM). We focus on the
weak long-range QSM, for which the thermodynamic limit is well-defined.
This model exhibits a continuous phase transition, separating a paramagnetic
from a ferromagnet phase. The universality class of the transition depends
on the long-range exponent α. We show that in the thermodynamic limit
the entanglement gap is finite in the paramagnetic phase, and it vanishes in
the ferromagnetic phase. In the ferromagnetic phase the entanglement gap
is understood in terms of standard magnetic correlation functions. The halfsystem entanglement gap decays as δξ ≃ CαL
−(1/2−α/4)
, where the constant
Cα depends on the low-energy properties of the model and L is the system
size. This reflects that the lower part of the dispersion is affected by the long
range physics. Finally, multiplicative logarithmic corrections are absent in the
scaling of the entanglement gap, in contrast with the higher-dimensional case