Entanglement entropy in Loop Quantum Gravity and geometrical area law
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909883959345152 |
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| author | Han, Muxin |
| author_facet | Han, Muxin |
| contents | The non-factorizing nature of the Hilbert space in Loop Quantum Gravity (LQG) due to gauge invariance requires a generalized definition of entanglement entropy. This work employs the framework of von Neumann algebras to investigate the entanglement entropy in LQG. On a graph, the holonomy and flux operators within a region and on the boundary generate a non-factor type I von Neumann algebra, which is used to define the entanglement entropy for LQG states. This algebraic formalism is applied to ``fixed-area states''--superpositions of spin networks associated with a surface with a definite macroscopic area given by the LQG area spectrum. By maximizing the entropy, we derive a geometrical area law where the entanglement entropy is proportional to the area. In addition, we show that bulk entanglement can renormalize the area-law coefficient and produce logarithmic corrections. The results in this paper closely relate to LQG black hole entropy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_26922 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entanglement entropy in Loop Quantum Gravity and geometrical area law Han, Muxin General Relativity and Quantum Cosmology High Energy Physics - Theory The non-factorizing nature of the Hilbert space in Loop Quantum Gravity (LQG) due to gauge invariance requires a generalized definition of entanglement entropy. This work employs the framework of von Neumann algebras to investigate the entanglement entropy in LQG. On a graph, the holonomy and flux operators within a region and on the boundary generate a non-factor type I von Neumann algebra, which is used to define the entanglement entropy for LQG states. This algebraic formalism is applied to ``fixed-area states''--superpositions of spin networks associated with a surface with a definite macroscopic area given by the LQG area spectrum. By maximizing the entropy, we derive a geometrical area law where the entanglement entropy is proportional to the area. In addition, we show that bulk entanglement can renormalize the area-law coefficient and produce logarithmic corrections. The results in this paper closely relate to LQG black hole entropy. |
| title | Entanglement entropy in Loop Quantum Gravity and geometrical area law |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.26922 |