Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model

• URL: http://arxiv.org/abs/2502.03093v1
• Date: Wed, 05 Feb 2025 11:32:59 GMT
• Title: Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model
• Authors: Barbara Jasser, Jovan Odavic, Alioscia Hamma,
• Abstract summary: We study the interplay between Stabilizer R'enyi Entropy (SRE) and entanglement entropy in both the ground state and highly excited states of the SYK4+SYK2 model. We find that SYK4 is indeed characterized by a complex pattern of both entanglement and non-stabilizer resources while SYK2 is non-universal and not complex.
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• Abstract: The Sachdev-Ye-Kitaev (SYK) model is of paramount importance for the understanding of both strange metals and a microscopic theory of two-dimensional gravity. We study the interplay between Stabilizer R\'enyi Entropy (SRE) and entanglement entropy in both the ground state and highly excited states of the SYK4+SYK2 model interpolating the highly chaotic four-body interactions model with the integrable two-body interactions one. The interplay between these quantities is assessed also through universal statistics of the entanglement spectrum and its anti-flatness. We find that SYK4 is indeed characterized by a complex pattern of both entanglement and non-stabilizer resources while SYK2 is non-universal and not complex. We discuss the fragility and robustness of these features depending on the interpolation parameter.

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