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Stabilizer Rényi Entropy and Its Transition in the Coupled Sachdev-Ye-Kitaev Model
Pengfei Zhang1,2, Shuyan Zhou1,3, Ning Sun1
1Fudan University, State Key Laboratory of Surface Physics and Department of Physics, Shanghai 200438, China.
Physical Review Letters
|March 13, 2026
Summary
This study introduces a new framework to analyze quantum magic using stabilizer Rényi entropy (SRE) in solvable quantum models. It reveals novel transitions undetectable by thermodynamics, advancing quantum phase analysis.
Area of Science:
- Quantum Information Science
- Condensed Matter Physics
- Theoretical Physics
Background:
- Quantum entanglement and quantum magic are key resources for complex quantum phenomena.
- Quantum magic, measured by stabilizer Rényi entropy (SRE), is hard to study beyond moderate system sizes.
- Existing research primarily uses numerical simulations for quantum magic.
Purpose of the Study:
- To establish a general framework for analyzing SRE in solvable Sachdev-Ye-Kitaev models.
- To enable the application of saddle-point approximation for SRE analysis.
- To explore quantum magic transitions in strongly correlated systems.
Main Methods:
- Developed a general framework for SRE analysis in large-N Sachdev-Ye-Kitaev models.
- Applied saddle-point approximation to the Maldacena-Qi coupled Sachdev-Ye-Kitaev model.
- Investigated SRE transitions by tuning temperature.
Main Results:
- Identified a series of first-order SRE transitions in the Maldacena-Qi model.
- Discovered an intrinsic SRE transition not detectable by thermodynamic quantities.
- Provided theoretical understanding of SRE in high- and low-temperature limits.
Conclusions:
- The framework allows studying SRE in strongly correlated fermionic systems in the thermodynamic limit.
- Introduced a new class of quantum phase transitions characterized by SRE.
- SRE can serve as a novel order parameter for quantum phase transitions.
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