Minimal Areas from Entangled Matrices
arXiv:2408.05274 · doi:10.21468/SciPostPhys.18.6.171
Abstract
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.
48+16 pages, 8 figures. v2: minor changes, journal version
References in corpus (40)
- The entropy of Hawking radiation
- Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information
- Deriving covariant holographic entanglement
- Large N algebras and generalized entropy
- Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial
- Embeddings and Integrable Charges for Extended Corner Symmetry
- Leading order corrections to the quantum extremal surface prescription
- Entanglement between Two Interacting CFTs and Generalized Holographic Entanglement Entropy
- Equivalence of approaches to relational quantum dynamics in relativistic settings
- Quantum Relativity of Subsystems
- A proposal for 3d quantum gravity and its bulk factorization
- Probing phase transitions of holographic entanglement entropy with fixed area states
- Enhanced corrections near holographic entanglement transitions: a chaotic case study
- Quantum reference frames, measurement schemes and the type of local algebras in quantum field theory
- Holographic entanglement entropy and the internal space
- Gauge Invariant Target Space Entanglement in D-Brane Holography
- Internal quantum reference frames for finite Abelian groups
- Bulk Entanglement Entropy and Matrices
- Matrix Quantization of Gravitational Edge Modes
- One-shot holography
- A note on the bulk interpretation of the Quantum Extremal Surface formula
- Diffeomorphism-invariant observables and dynamical frames in gravity: reconciling bulk locality with general covariance
- Entanglement in the Quantum Hall Matrix Model
- Gravitational entropy is observer-dependent
- Multipartite edge modes and tensor networks
- Mutual information on the fuzzy sphere
- Entanglement Entropy in Internal Spaces and Ryu-Takayanagi Surfaces
- Boundary Description of Microstates of the Two-Dimensional Black Hole
- Emergent Area Laws from Entangled Matrices
- Blocking up D-branes : Matrix renormalization ?
- Quantum Frame Relativity of Subsystems, Correlations and Thermodynamics
- On the Charge Algebra of Causal Diamonds in Three Dimensional Gravity
- Coarse-graining quivers
- A New Covariant Entropy Bound from Cauchy Slice Holography
- Extremality as a Consistency Condition on Subregion Duality
- Counting states in a model of replica wormholes
- Bit models of replica wormholes
- Entanglement Edge Modes of General Noncommutative Matrix Backgrounds
- APD-Invariant Tensor Networks from Matrix Quantum Mechanics
- A clock is just a way to tell the time: gravitational algebras in cosmological spacetimes