Entanglement Structure of Nonlocal Field Theories

Nonlocal interactions are known to generate volume-law entanglement entropy. However, their deeper impact on the fine structure of quantum correlations remains a key open question. In this work, we explore a bosonic nonlocal field theory, examining correlation measures beyond entanglement entropy, namely, mutual information and tripartite information. Using numerical lattice simulations, we show that the nonlocality scale, A, not only determines the onset of volume-law behavior but also leads to striking features: notably, extremely long-range mutual information and an unusual monogamy structure. In this regime, increasing the separation between large regions can paradoxically enhance their multipartite entanglement. Through holographic duality, we verify that the Ryu-Takayanagi formula correctly captures the volume-law scaling of entropy. Yet, a significant tension emerges: while the field theory reveals rich spatial correlations, the holographic model predicts a complete suppression of both mutual and tripartite information in the volume-law phase. This non-monogamous behavior in the holographic description stands in sharp contrast to the monogamous and highly structured entanglement observed in the field theory. Our results demonstrate that nonlocality gives rise to quantum states of such complexity that conventional geometric models of spacetime fall short. This points to the need for a new framework that goes beyond geometry to fully capture the nature of these correlations.