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Matrix Quantum Mechanics and Entanglement Entropy: A Review
Jackson R Fliss1,2, Alexander Frenkel3
1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK.
Entropy (Basel, Switzerland)
|January 28, 2026
Summary
This study explores entanglement entropy in matrix quantum mechanics (MQM) at large N. It connects MQM to string theory and non-commutative geometry, revealing an
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.
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