Entanglement gap in 1D long-range quantum spherical models

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