The study of quantum criticality and entanglement in systems with long-range (LR) interactions is still in its early stages, with many open questions remaining to be explored. In this work, we investigate critical exponents and scaling of entanglement entropy (EE) in the LR bilayer Heisenberg model using large-scale quantum Monte Carlo simulations. By applying modified (standard) finite-size scaling above (below) the upper critical dimension and field theory analysis, we obtain precise critical exponents in three regimes: the LR Gaussian regime with a Gaussian fixed point, the short-range (SR) regime with Wilson-Fisher exponents, and a LR non-Gaussian regime where the critical exponents vary continuously from LR Gaussian to SR values. We compute the Rényi EE both along the critical line and in the Néel phase, and we observe that as the LR interaction is enhanced, the area-law contribution in EE gradually vanishes both at quantum critical points (QCPs) and in the Néel phase. The log-correction in EE arising from sharp corners at the QCPs also decays to zero as the LR interaction grows, whereas that for Néel states, caused by the interplay of Goldstone modes and restoration of the symmetry in a finite system, is enhanced. Relevant experimental settings to detect these nontrivial properties for quantum many-body systems with LR interactions are discussed.

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• Entanglement entropy
• Long-range interactions
• Bilayer films
• Quantum spin models
• Conformal field theory
• Critical exponents
• Heisenberg model
• Quantum Monte Carlo