Genuine Multipartite Entanglement in the quantum Ising model

Genuine multipartite entanglement (GME) provides a powerful tool to explore quantum critical phenomena in quantum Ising models. We introduce a new protocol, entanglement microscopy, to analyze both bipartite and multipartite entanglement across 1D, 2D, and 3D transverse field Ising models, with a focus on GME. Our results show that entanglement, including GME, decays rapidly with separation, revealing its local nature in all dimensions. Additionally, GME peaks near the quantum critical point (QCP) as a function of the transverse field, demonstrating its effectiveness as a probe for quantum phase transitions. Lastly, GME decreases with increasing dimension, reflecting the monogamy of entanglement. These findings offer insights into the dimension-dependent entanglement structure in quantum Ising models, emphasizing GME’s role in capturing critical behavior.