Phase transitions and critical scaling in a long-range interacting XXZ spin chain

In this paper, we investigate Quantum Phase Transitions (QPTs) in the long-range XXZ spin chain using two information-theoretic probes: The half-chain entanglement entropy and a witness of genuine multipartite nonlocality. Both quantities effectively identify the phase boundary, but exhibit distinct scaling behaviors: the entanglement entropy grows linearly with system size N, while the multipartite nonlocality increases exponentially, with [Formula: see text]. By independently tuning the power-law decay exponents of the transverse ([Formula: see text]) and longitudinal ([Formula: see text]) couplings, we uncover contrasting trends in the critical point [Formula: see text]: Increasing [Formula: see text] shifts it to larger values, while increasing [Formula: see text] shifts it to smaller ones. These monotonic and saturating dependencies are captured by an empirical exponential model, offering a compact and physically transparent description of the critical behavior. Our results highlight the crucial role of interaction range in driving criticality, with implications for engineered quantum systems and long-range entanglement control.