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

• URL: http://arxiv.org/abs/2509.17417v2
• Date: Tue, 23 Sep 2025 12:55:35 GMT
• Title: Stabilizer Rényi Entropy and its Transition in the Coupled Sachdev-Ye-Kitaev Model
• Authors: Pengfei Zhang, Shuyan Zhou, Ning Sun,
• Abstract summary: We study the study of quantum magic using the stabilizer R'enyi entropy (SRE)<n>We uncover an intrinsic transition of the SRE that cannot be detected through thermodynamic quantities.<n>Our results pave the way for studying the SRE in strongly correlated fermionic systems in the thermodynamic limit.
• Score: 21.14519574861178
• License: http://creativecommons.org/licenses/by/4.0/
• 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 R\'enyi 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 (SYK) models in the large-$N$ limit, which enables the application of the saddle-point approximation. Applying this method to the Maldacena-Qi coupled SYK 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.

Related papers

• SYK thermal expectations are classically easy at any temperature [49.788604174558564]
  We give a simple classical algorithm that approximates thermal expectations.<n>We show it has quasi-polynomial cost $nO(log n/)$ for all temperatures above a phase transition in the free energy.
  arXiv  Detail & Related papers  (2026-02-26T04:48:32Z)
• Two-Point Stabilizer Rényi Entropy: a Computable Magic Proxy of Interacting Fermions [0.17478203318226307]
  Quantifying non-stabilizerness (magic'') in interacting fermionic systems remains a formidable challenge.<n>We establish the two-point stabilizer Rényi entropy (SRE) and its mutual counterpart as robust, computationally accessible probes for detecting magic in diverse fermionic phases.<n>Our results validate the two-point SRE as a versatile and sensitive diagnostic, forging a novel link between quantum resource theory, critical phenomena, and topological order in strongly correlated matter.
  arXiv  Detail & Related papers  (2026-01-19T19:00:03Z)
• Path integral approach to quantum thermalization [39.25860941747971]
  We introduce a quasiclassical Green function approach describing the unitary yet irreversible dynamics of quantum systems.<n>We show that it is capable of describing a wide range of system classes and disorder models.<n>We present our formalism in a self-contained and pedagogical manner, aiming to provide a transferable toolbox for the first-principles description of many-body chaotic quantum systems.
  arXiv  Detail & Related papers  (2025-09-07T12:10:48Z)
• Stabilizer Rényi Entropy for Translation-Invariant Matrix Product States [2.930915232771767]
  R'enyi entropy (SRE) offers a tractable measure of magic, avoiding the complexity of conventional methods.<n>We numerically reveal a fundamental connection between magic and entanglement, thereby paving the way for deeper theoretical investigations into their interplay.
  arXiv  Detail & Related papers  (2025-08-05T15:04:03Z)
• Nonstabilizerness in the unitary and monitored quantum dynamics of XXZ-staggered and SYK models [0.0]
  We consider the quantum-state-diffusion dynamics of the XXZ-staggered spin chain.<n>We evaluate the nonstabilizerness (also known as magic'') along the trajectories, quantified through the stabilizer R'enyi entropy (SRE)<n>In the absence of measurements, we find that the SYK model is the only one in which the time-averaged SRE saturates the random state bound.
  arXiv  Detail & Related papers  (2025-02-03T15:11:42Z)
• Thermalization and Criticality on an Analog-Digital Quantum Simulator [133.58336306417294]
  We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions. We digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization.
  arXiv  Detail & Related papers  (2024-05-27T17:40:39Z)
• Exact solution of long-range stabilizer Rényi entropy in the dual-unitary XXZ model [0.0]
  We study the generation of magic under evolution by a quantum circuit. We focus on the dual-unitary XXZ model and a measure of magic called stabilizer R'enyi entropy (SRE)
  arXiv  Detail & Related papers  (2024-05-07T16:13:45Z)
• Magic in generalized Rokhsar-Kivelson wavefunctions [0.0]
  We study magic, as quantified by the stabilizer Renyi entropy, in a class of models known as generalized Rokhsar-Kive systems. We find that the maximum of the SRE generically occurs at a cusp away from the quantum critical point, where the derivative suddenly changes sign.
  arXiv  Detail & Related papers  (2023-11-14T19:00:05Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive [52.77024349608834]
  We present a self consistent field approach (SCF) within the Adaptive Derivative-Assembled Problem-Assembled Ansatz Variational Eigensolver (ADAPTVQE) This framework is used for efficient quantum simulations of chemical systems on nearterm quantum computers.
  arXiv  Detail & Related papers  (2022-12-21T23:15:17Z)
• Indication of critical scaling in time during the relaxation of an open quantum system [34.82692226532414]
  Phase transitions correspond to the singular behavior of physical systems in response to continuous control parameters like temperature or external fields. Near continuous phase transitions, associated with the divergence of a correlation length, universal power-law scaling behavior with critical exponents independent of microscopic system details is found.
  arXiv  Detail & Related papers  (2022-08-10T05:59:14Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.