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arXiv · 2512.03163

Matrix Quantum Mechanics and Entanglement Entropy: A Review

Jackson R. Fliss·Alexander Frenkel
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Abstract

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.

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Jackson R. Fliss, Alexander Frenkel. 2025-12-02. Matrix Quantum Mechanics and Entanglement Entropy: A Review. https://arxiv.org/abs/2512.03163

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