Matrix Quantum Mechanics and Entanglement Entropy: A Review
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915650791800832 |
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| author | Fliss, Jackson R. Frenkel, Alexander |
| author_facet | Fliss, Jackson R. Frenkel, Alexander |
| contents | We review aspects of entanglement entropy in the quantum mechanics of $N\times N$ matrices, i.e. matrix quantum mechanics (MQM), at large $N$. In doing so we review standard models of MQM and their relation to string theory, D-brane physics, and emergent non-commutative geometries. We overview, in generality, definitions of subsystems and entanglement entropies in theories with gauge redundancy and discuss the additional structure required for definining subsystems in MQMs possessing a $U(N)$ gauge redundancy. In connecting these subsystems to non-commutative geometry, we review several works on `target space entanglement,' and entanglement in non-commutative field theories, highlighting the conditions in which target space entanglement entropy displays an `area law' at large $N$. We summarize several example calculations of entanglement entropy in non-commutative geometries and MQMs. We review recent work in connecting the area law entanglement of MQM to the Ryu-Takayanagi formula, highlighting the conditions in which $U(N)$ invariance implies a minimal area formula for the entanglement entropy at large $N$. Finally, we make comments on open questions and research directions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_03163 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matrix Quantum Mechanics and Entanglement Entropy: A Review Fliss, Jackson R. Frenkel, Alexander High Energy Physics - Theory We review aspects of entanglement entropy in the quantum mechanics of $N\times N$ matrices, i.e. matrix quantum mechanics (MQM), at large $N$. In doing so we review standard models of MQM and their relation to string theory, D-brane physics, and emergent non-commutative geometries. We overview, in generality, definitions of subsystems and entanglement entropies in theories with gauge redundancy and discuss the additional structure required for definining subsystems in MQMs possessing a $U(N)$ gauge redundancy. In connecting these subsystems to non-commutative geometry, we review several works on `target space entanglement,' and entanglement in non-commutative field theories, highlighting the conditions in which target space entanglement entropy displays an `area law' at large $N$. We summarize several example calculations of entanglement entropy in non-commutative geometries and MQMs. We review recent work in connecting the area law entanglement of MQM to the Ryu-Takayanagi formula, highlighting the conditions in which $U(N)$ invariance implies a minimal area formula for the entanglement entropy at large $N$. Finally, we make comments on open questions and research directions. |
| title | Matrix Quantum Mechanics and Entanglement Entropy: A Review |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.03163 |