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arXiv:2606.05757

Detecting Topological Transitions and Anisotropy through Multipartite Entanglement in Holographic Weyl Semimetals

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

Published Jun 4, 2026• 0 citations
arXivHTMLPDF

Abstract

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 $κ$ and the Markov gap, multi-EWCS, and two multi-EWCS based four-partite signals $Δ$ and $g$. These quantities are studied as functions of the strip width $l$ and the tuning parameter across the topological transition. At large $l$, their $l$ dependence takes a power-law form governed by the IR scaling of the system. At fixed large $l$, 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.

DOI
10.48550/arxiv.2606.05757

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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.
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.
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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.
A bstract We investigate how IR modifications of the bulk geometry reshape long-range multipartite entanglement on the boundary in holography. We modify the IR geometries in two opposite directions: spherical modifications that enhance long-range entanglement and hyperbolic modifications that suppress them. We utilize various multipartite entanglement measures/signals to analyze the multipartite entanglement structures. These measures/signals are combinations of entanglement entropy, multi-entropy, entanglement wedge cross sections (EWCS) and multi-EWCS. Our results reveal that in the extremal limits of these two geometric modifications, the multipartite entanglement structures exhibit starkly contrasting behaviors: various measures saturate either their theoretical upper or lower bounds in the respective geometries. This demonstrates that IR deformations provide a practical holographic framework for realizing extremal entanglement regimes. Moreover, it serves as an effective tool for studying quantum marginal problems in holography. Finally, by observing how different measures respond to these engineered geometries, we gain clarifying insights into the specific types of multipartite entanglement that each measure/signal is particularly sensitive to.