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Minimal Areas from Entangled Matrices

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arxiv 2408.05274 v2 pith:V3WYMTYD submitted 2024-08-09 hep-th gr-qcquant-ph

Jackson R. Fliss , Alexander Frenkel , Sean A. Hartnoll , Ronak M Soni This is my paper · ORCID
classification hep-thgr-qcquant-ph
keywords entanglementmatricescorrespondingdefineformulageometryminimalquantum
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We define a relational notion of a subsystem in theories of matrix quantum mechanics and show how the corresponding entanglement entropy can be given as a minimisation, exhibiting many similarities to the Ryu-Takayanagi formula. Our construction brings together the physics of entanglement edge modes, noncommutative geometry and quantum internal reference frames, to define a subsystem whose reduced state is (approximately) an incoherent sum of density matrices, corresponding to distinct spatial subregions. We show that in states where geometry emerges from semiclassical matrices, this sum is dominated by the subregion with minimal boundary area. As in the Ryu-Takayanagi formula, it is the computation of the entanglement that determines the subregion. We find that coarse-graining is essential in our microscopic derivation, in order to control the proliferation of highly curved and disconnected non-geometric subregions in the sum.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Relational entanglement entropies and quantum reference frames in gauge theories

    hep-th 2025-06 accept novelty 7.0 of 10

    Quantum reference frames built from Wilson lines give lattice gauge theories gauge-invariant subsystem factorizations and a hierarchy of relational entanglement entropies.

  2. York time in JT gravity

    hep-th 2025-05 conditional novelty 7.0 of 10

    In JT gravity, the Hartle-Hawking wavefunction satisfies a Schrodinger equation in York time with a Hermitian squeezing Hamiltonian, and York time evolution is a unitary change of the length basis rather than physical...

  3. Soft edges: the many links between soft and edge modes

    hep-th 2024-12 conditional novelty 7.0 of 10

    In Maxwell theory, asymptotically charged edge modes (soft edges) pull asymptotic symmetries and soft data into finite subregions, giving finite-distance corner charges without an infinite-volume limit.

  4. Entanglement Entropy of Quantum Corners

    hep-th 2025-07 conditional novelty 6.0 of 10

    For a two-dimensional corner symmetry algebra, coherent corner states give an entanglement entropy that scales with the area when mapped to near-extremal Reissner-Nordström black holes.

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