Non-stabilizerness of Sachdev-Ye-Kitaev model, by Surajit Bera, Marco Schirò
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SciPost Physics Home Authoring Refereeing Submit a manuscript About Non-stabilizerness of Sachdev-Ye-Kitaev model Surajit Bera, Marco Schirò SciPost Phys. 19, 159 (2025) · published 18 December 2025 doi: 10.21468/SciPostPhys.19.6.159 pdf BiBTeX RIS Submissions/Reports Abstract We study the non-stabilizerness or quantum magic of the Sachdev-Ye-Kitaev ($\mathrm{SYK}$) model, a prototype example of maximally chaotic quantum matter. We show that the Majorana spectrum of its ground state, encoding the spreading of the state in the Majorana basis, displays a Gaussian distribution as expected for chaotic quantum many-body systems. We compare our results with the case of the $\mathrm{SYK_2}$ model, describing non-chaotic random free fermions, and show that the Majorana spectrum is qualitatively different in the two cases, featuring an exponential Laplace distribution for the $\mathrm{SYK_2}$ model rather than a Gaussian. From the spectrum we extract the Stabilizer Renyi Entropy (SRE) and show that for both models it displays a linear scaling with system size, with a prefactor that is larger for the SYK model, which has therefore higher magic. Finally, we discuss the spreading of quantun magic under unitary dynamics, as described by the evolution of the Majorana spectrum and the Stabilizer Renyi Entropy starting from a stabilizer state. We show that the SRE for the $\mathrm{SYK_2}$ model equilibrates rapidly, but that in the steady-state the interacting chaotic SYK model has more magic than the simple $\mathrm{SYK_2}$. Our results suggest that the Majorana spectrum is qualitatively distinct in chaotic and non-chaotic many-body systems. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.19.6.159TI - Non-stabilizerness of Sachdev-Ye-Kitaev modelPY - 2025/12/18UR - https://scipost.org/SciPostPhys.19.6.159JF - SciPost PhysicsJA - SciPost Phys.VL - 19IS - 6SP - 159A1 - Bera, SurajitAU - Schirò, MarcoAB - We study the non-stabilizerness or quantum magic of the Sachdev-Ye-Kitaev ($\mathrm{SYK}$) model, a prototype example of maximally chaotic quantum matter. We show that the Majorana spectrum of its ground state, encoding the spreading of the state in the Majorana basis, displays a Gaussian distribution as expected for chaotic quantum many-body systems. We compare our results with the case of the $\mathrm{SYK_2}$ model, describing non-chaotic random free fermions, and show that the Majorana spectrum is qualitatively different in the two cases, featuring an exponential Laplace distribution for the $\mathrm{SYK_2}$ model rather than a Gaussian. From the spectrum we extract the Stabilizer Renyi Entropy (SRE) and show that for both models it displays a linear scaling with system size, with a prefactor that is larger for the SYK model, which has therefore higher magic. Finally, we discuss the spreading of quantun magic under unitary dynamics, as described by the evolution of the Majorana spectrum and the Stabilizer Renyi Entropy starting from a stabilizer state. We show that the SRE for the $\mathrm{SYK_2}$ model equilibrates rapidly, but that in the steady-state the interacting chaotic SYK model has more magic than the simple $\mathrm{SYK_2}$. Our results suggest that the Majorana spectrum is qualitatively distinct in chaotic and non-chaotic many-body systems.ER - × @Article{10.21468/SciPostPhys.19.6.159, title={{Non-stabilizerness of Sachdev-Ye-Kitaev model}}, author={Surajit Bera and Marco Schirò}, journal={SciPost Phys.}, volume={19}, pages={159}, year={2025}, publisher={SciPost}, doi={10.21468/SciPostPhys.19.6.159}, url={https://scipost.org/10.21468/SciPostPhys.19.6.159},} Ontology / Topics See full Ontology or Topics database. Exact diagonalization Monte-Carlo simulations Quantum chaos Quantum information Quantum many-body systems Authors / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 2 3 Surajit Bera, 1 2 3 Marco Schirò 1 Collège de France 2 Centre National de la Recherche Scientifique / French National Centre for Scientific Research [CNRS] 3 Université de recherche Paris Sciences et Lettres / PSL Research University [PSL] Funders for the research work leading to this publication Collège de France Horizon 2020 (through Organization: European Commission [EC])