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  • Open Access

Stabilizer Rényi Entropy and Its Transition in the Coupled Sachdev-Ye-Kitaev Model

Pengfei Zhang1,2,*, Shuyan Zhou1,3, and Ning Sun1,†

  • 1State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200438, China
  • 2Hefei National Laboratory, Hefei 230088, China
  • 3Department of Physics and Center for Theory of Quantum Matter, University of Colorado Boulder, Boulder, Colorado 80309, USA

  • *Contact author: PengfeiZhang.physics@gmail.com
  • †Contact author: ningsun.atom@gmail.com
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Phys. Rev. Lett. 136, 080201 – Published 23 February, 2026

DOI: https://doi.org/10.1103/5c15-4g5n

Abstract

Quantum entanglement and quantum magic are two distinct fundamental resources that enable quantum systems to exhibit complex phenomena beyond the capabilities of classical computer simulations. While quantum entanglement has been extensively used to characterize both equilibrium and dynamical phases, the study of quantum magic, typically quantified by the stabilizer Rényi entropy (SRE), remains largely limited to numerical simulations of moderate system sizes. In this Letter, we establish a general framework for analyzing the SRE in solvable Sachdev-Ye-Kitaev models in the large-N limit, which enables the application of the saddle-point approximation. Applying this method to the Maldacena-Qi coupled Sachdev-Ye-Kitaev model, we identify a series of first-order transitions of the SRE as the temperature is tuned. In particular, we uncover an intrinsic transition of the SRE that cannot be detected through thermodynamic quantities. We also discuss the theoretical understanding of the SRE in both the high-temperature and low-temperature limits. Our results pave the way for studying the SRE in strongly correlated fermionic systems in the thermodynamic limit and suggest a new class of transitions for which the SRE serves as an order parameter.

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Phys. Rev. Lett. 136, 080201– Published 23 February, 2026
  • Received 27 September 2025
  • Revised 12 December 2025
  • Accepted 6 February 2026
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