We examine the holographic entanglement entropy in hyperscaling violating backgrounds. Precisely in such theories, by semianalytic computation, we use holographic methods to derive the universal terms of entanglement entropy in various dimensions. We also find such terms when the bulk action includes higher-order curvature terms. We make further comments on the mutual information in hyperscaling violating backgrounds with higher curvature interactions. We explore the sign of tripartite information, which results in a monogamy property on mutual information. It is shown that for various hyperscaling parameters, the mutual and tripartite information are always positive and negative, respectively. This indicates that mutual information is monogamous in theories with hyperscaling violation.
To analyze the holographic multipartite entanglement structure, we study the upper bound for holographic
n-partite information
(−1)nIn that
n−1 fixed boundary subregions participate together with an arbitrary region
E. In general cases, we could find regions
E that make
In approach the upper bound. For
n=3, we show that the upper bound of
−I3 is given by a quantity that we name the entanglement of state-constrained purification
EoSP(A:B). For
n≥4, we find that the upper bound of
In is finite in holographic CFT
1+1 but has UV divergences in higher dimensions, which reveals a fundamental difference in the entanglement structure in different dimensions. When
(−1)nIn reaches the information-theoretical upper bound, we argue that ( I_n ) fully accounts for multipartite global entanglement in these upper bound critical points, in contrast to usual cases where
In is not a perfect measure for multipartite entanglement. We further show that these results suggest that fewer-partite entanglement fully emerges from more-partite entanglement, and any
n−1 distant regions are fully
n-partite entangling in higher dimensions.
A bstract The n -partite information (nI) is formulated as a measure of multi-partite entanglement. Field theory computation revealed that the sign of nI is indefinite for n ≥ 3, while holographic studies conjectured a sign property that holographic nI is non-negative/non-positive for even/odd n , with tripartite information (TI, n = 3) proved. We investigate the aspects of nI with holographic duality in hyperscaling violating geometry. We confirm the conjectured sign property for strips of equal length with equal separation distance, and disprove this conjecture for n > 3 with general configurations. Therefore, nI in field theories and holography exhibits compatibility except for n = 3. We also discuss other properties of holographic nI with analytic computation: the monotonicity, linearity, relation to hyperscaling violating parameters, temperature and UV cutoff effects, and the physical implications. It is doubtful that nI is an effective measure of entanglement considering the indefinite sign, non-monotonicity, and quasi-linearity of its holographic dual. In this respect, we propose constraints on the multi-partite entanglement measures.
A bstract We propose a signal
Δp(3) ∆ p 3 for tripartite correlations in finite-dimensional quantum systems and
Δw(3) ∆ w 3 for holographic systems. We prove that
Δp(3) ∆ p 3 is non-negative for any tripartite entangled mixed states and vanishes for mixed product states. It is a correlation signal because it is generally nonzero for a separable state containing a classical mixture. Based on the conjecture, the equality between an entanglement wedge cross section E w and entanglement of purification E p , i.e., E w = E P in the semiclassical limit, we apply the tripartite correlation signal to study the structures of tripartite entanglement in AdS 3 /CFT 2 , especially for pure AdS 3 . We comment on a generalization to n -partite correlation signals
Δp(n)(A1:⋯:An) Δ p n A 1 : ⋯ : A n .
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.
Topological states of matter are characterized by nonlocal structures that are naturally encoded in the quantum entanglement of many-body wavefunctions. Topological semimetals are short-range entangled states at weak coupling and their entanglement structure at strong coupling remains largely unexplored. In this work, we investigate the multipartite entanglement structure of strongly coupled holographic nodal line semimetals. Building on previous studies of entanglement entropy and the holographic c-function, we focus on multipartite entanglement measures, including the conditional mutual information, multi-entropy, and the Markov gap which is based on the entanglement wedge cross section. Our results demonstrate that while these multipartite measures vanish in the long-distance limit
l→∞, which confirms that the holographic nodal line semimetal remains a short-range entangled state, their large
l scaling behavior remains highly sensitive to the underlying topology. The large
l power-law decay and scaling exponents serve as robust, non-local order parameters that exhibit sharp changes at the quantum critical point. This work establishes multi-partite entanglement as a powerful probe of quantum topological phase transitions in strongly coupled topological systems.