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arXiv:2608.09056

Long-range multipartite entanglement in holographic gapless systems

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

Published Aug 10, 2026• 0 citations
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Abstract

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 \(\mathrm{AdS}_{3}\times\mathbb{R}^{2}\), 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.

DOI
10.48550/arxiv.2608.09056

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We investigate how the junction law for multipartite entanglement is realized in confining holographic backgrounds, using genuine multi-entropy (GM) as our main diagnostic. We first study an AdS3_33​ hard-wall toy model as an analytic benchmark, where multi-way cuts and junction geometries can be analyzed explicitly. In this setup, we classify the relevant saddles, determine the dominant phases, and show that the genuinely multipartite contribution diagnosed by GM is localized near the junction. We also examine how this structure depends on subsystem sizes, asymmetry, and the confinement scale, including phase transitions between competing saddles. We then move beyond the hard-wall benchmark to smooth confining geometries, focusing on the D4-soliton and D3-soliton backgrounds and formulating the corresponding framework also for the Klebanov--Strassler background. In the smooth-cap examples, we find that the junction picture persists, while the detailed phase structure differs from the hard-wall case: in particular, the hard-wall plateau does not survive, and GM instead decreases monotonically and vanishes at a finite critical scale. We also find that the short-distance behavior is background-dependent, with GM(3)∼L−4\mathrm{GM}^{(3)}\sim L^{-4}GM(3)∼L−4 in the D4-soliton background, GM(3)∼L−2\mathrm{GM}^{(3)}\sim L^{-2}GM(3)∼L−2 in the D3-soliton background, and GM(3)∼L−2⋅(log⁡L)2\mathrm{GM}^{(3)}\sim L^{-2}\cdot (\log L)^{2}GM(3)∼L−2⋅(logL)2 in the Klebanov--Strassler background. These results clarify which features of the junction-law picture are robust in confining holography and which features of the phase structure and short-distance scaling are background-dependent.
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