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arXiv:2602.01545

Multipartite entanglement characterizing topological phase transitions in holographic nodal line semimetals

X. R. Chen, Xuanting Ji, Ya-Wen Sun

Published Feb 2, 2026• 0 citations
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Abstract

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 $l \to \infty$, 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.

DOI
10.48550/arxiv.2602.01545

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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→∞l \to \inftyl→∞, which confirms that the holographic nodal line semimetal remains a short-range entangled state, their large lll scaling behavior remains highly sensitive to the underlying topology. The large lll 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.
A bstract 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.
We study multipartite entanglement structures in the zero-temperature holographic Weyl semimetal, focusing on tripartite and four-partite structures. For strip regions, we compute the conditional mutual information, the entanglement wedge cross section, tripartite measures κκκ and the Markov gap, multi-EWCS, and two multi-EWCS based four-partite signals ΔΔΔ and ggg. These quantities are studied as functions of the strip width lll and the tuning parameter across the topological transition. At large lll, their lll dependence takes a power-law form governed by the IR scaling of the system. At fixed large lll, all these entanglement quantities develop clear features near the critical point, showing that tripartite and four-partite entanglement structures can diagnose the topological quantum phase transition. We further study strips pointing in different directions to probe the anisotropy of the system. The anisotropic large l behavior distinguishes the nontrivial phase from the trivial phase. These results establish multipartite holographic entanglement as a sensitive, nonlocal probe of topological phase transitions and anisotropic IR physics.
Abstract Topological semimetals are a class of many-body systems exhibiting novel macroscopic quantum phenomena at the interplay between high energy and condensed matter physics. They display a topological quantum phase transition (TQPT) which evades the standard Landau paradigm. In the case of Weyl semimetals, the anomalous Hall effect is a good non-local order parameter for the TQPT, as it is proportional to the separation between the Weyl nodes in momentum space. On the contrary, for nodal line semimetals (NLSM), the quest for an order parameter is still open. By taking advantage of a recently proposed holographic model for strongly-coupled NLSM, we explicitly show that entanglement entropy (EE) provides an optimal probe for nodal topology. We propose a generalized c-function, constructed from the EE, as an order parameter for the TQPT. Moreover, we find that the derivative of the renormalized EE with respect to the external coupling driving the TQPT diverges at the critical point, signaling the rise of non-local quantum correlations. Finally, we show that these quantum information quantities are able to characterize not only the critical point but also features of the quantum critical region at finite temperature.
Gapless quantum systems support correlations over arbitrarily long distances, giving rise to power-law long-range entanglement. We investigate long-range entanglement at strong coupling for three-dimensional gapless systems using holography, asking whether multipartite entanglement can exhibit scale-growing behavior and become enhanced at large distances. We show that a broad class of multipartite entanglement quantities share the same leading large-distance scaling exponent determined by the IR geometry. To realize different scaling regimes, we consider hyperscaling-violating IR geometries. Depending on the parameters, long-distance multipartite entanglement can decay, become logarithmic, grow subextensively, or reach a volume law. We also analyze an anisotropic IR geometry AdS3×R2\mathrm{AdS}_{3}\times\mathbb{R}^{2}AdS3​×R2, where long-range multipartite entanglement survives along one direction but becomes short-ranged in the transverse gapped directions. These results show that holographic gapless phases can support rich and enhanced long-range multipartite entanglement, providing a nonlocal characterization of the underlying IR physics.
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, AAA, 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.
This paper contains discussions on the entanglement entropy and mutual information of a strongly coupled field theory with a critical point which has a holographic dual. We investigate analytically, in the specific regimes of parameters, how these nonlocal operators behave near the critical point. Interestingly, we observe that although the mutual information is constant at the critical point, its slope shows a power-law divergence in the vicinity of the critical point. We show that the leading behavior of mutual information at and near the critical point could yield a set of critical exponents if we regard it as an order parameter. Our result for this set of static critical exponents is (1/2,1/2,1/2,2)(1/2,1/2,1/2,2)(1/2,1/2,1/2,2) which is identical to the one calculated via the thermodynamic quantities. Hence it suggests that beside the numerous merits of mutual information, this quantity also captures the critical behavior of the underlying field theory and it could be used as a proper measure to probe the phase structure associated with the strongly coupled systems.