  We investigate the finite-size scaling of the entanglement gap in the one
dimensional 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 $\alpha$. 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
entanglement gap decays as $\delta\xi\simeq C_\alpha L^{-(1/2-\alpha/4)}$,
where the constant $C_\alpha$ depends on the low-energy properties of the
model. 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.
