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arXiv · 2512.15256

Quantum Entanglement of Anyonic Charges and Emergent Spacetime Geometry

Hoang-Anh Le·Hyun Cheol Lee·S. -R. Eric Yang
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Abstract

Intrinsically topologically ordered phases can host anyons. Here, we take the view that entanglement between anyons can give rise to an emergent geometry resembling Anti-de Sitter (AdS) space. We analyze the entanglement structure of fractionalized anyons using mutual information and interpret the results within this emergent geometric framework. As a concrete example, we consider pairs of $e/2$-charged semions that arise from instanton configurations in a disordered zigzag graphene nanoribbon. These fractional charges, located on opposite zigzag edges, show long-range quantum entanglement despite being spatially separated. We analyze the scale dependence of their entanglement and embed the ribbon into an AdS-like bulk geometry. In this setup, the entanglement structure defines minimal surfaces in the bulk, providing a geometric view of the edge correlations. This gives a holographic picture of fractionalized degrees of freedom in quasi-one-dimensional systems and shows how quantum entanglement can generate emergent geometry even without conformal symmetry.

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Hoang-Anh Le, Hyun Cheol Lee, S. -R. Eric Yang. 2025-12-17. Quantum Entanglement of Anyonic Charges and Emergent Spacetime Geometry. https://doi.org/10.1088/1367-2630%2Fae3a0b

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