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Matrix Quantum Mechanics and Entanglement Entropy: A Review.

Jackson R Fliss^1,2, Alexander Frenkel³

¹Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK.

Entropy (Basel, Switzerland)

|January 28, 2026

Summary

This summary is machine-generated.

This study explores entanglement entropy in matrix quantum mechanics (MQM) at large N. It connects MQM to string theory and non-commutative geometry, revealing an

Keywords:

entanglement entropy large N matrix quantum mechanics

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Area of Science:

Quantum Information Theory
String Theory
Condensed Matter Physics

Background:

Matrix quantum mechanics (MQM) is a theoretical framework with connections to string theory and D-brane physics.
Understanding entanglement entropy is crucial for quantum information theory and quantum gravity.
Non-commutative geometries offer a novel perspective on quantum systems.

Purpose of the Study:

To review and synthesize current research on entanglement entropy within matrix quantum mechanics (MQM) at large N.
To explore the relationship between MQM, string theory, and emergent non-commutative geometries.
To investigate the definition and calculation of entanglement entropy in gauge theories with redundancy.

Main Methods:

Review of existing literature on MQM, string theory, and non-commutative geometry.
Analysis of definitions for subsystems and entanglement entropies in gauge theories.
Examination of 'target space entanglement' and its properties in non-commutative field theories.
Summarization of example calculations for entanglement entropy in MQMs and non-commutative geometries.

Main Results:

Entanglement entropy in MQM at large N can exhibit an 'area law' under specific conditions.
The study highlights the connection between target space entanglement and non-commutative geometry.
A link is established between the area law in MQM and the Ryu-Takayanagi formula, particularly with U(N) invariance.

Conclusions:

The 'area law' for entanglement entropy in MQM is consistent with holographic principles at large N.
U(N) invariance in MQM naturally leads to a minimal area formula for entanglement entropy.
Further research is needed to address open questions regarding entanglement entropy in these complex quantum systems.