Quantum Entanglement of Anyonic Charges and Emergent Spacetime Geometry
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918309927059456 |
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| author | Le, Hoang-Anh Lee, Hyun Cheol Yang, S. -R. Eric |
| author_facet | Le, Hoang-Anh Lee, Hyun Cheol Yang, S. -R. Eric |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_15256 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Entanglement of Anyonic Charges and Emergent Spacetime Geometry Le, Hoang-Anh Lee, Hyun Cheol Yang, S. -R. Eric Strongly Correlated Electrons General Relativity and Quantum Cosmology High Energy Physics - Theory 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. |
| title | Quantum Entanglement of Anyonic Charges and Emergent Spacetime Geometry |
| topic | Strongly Correlated Electrons General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.15256 |