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Nonstabilizerness Dynamics in Many-Body Localized Systems.

Pedro R Nicácio Falcão1,2, Piotr Sierant3, Jakub Zakrzewski2,4

  • 1Uniwersytet Jagielloński, Szkoła Doktorska Nauk Ścisłych i Przyrodniczych, Łojasiewicza 11, PL-30-348 Kraków, Poland.

Physical Review Letters
|January 2, 2026
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Summary
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Nonstabilizerness, a measure of quantum complexity, grows with interactions in disordered many-body localized systems, unlike in ergodic systems. This study reveals a universal scaling relationship with entanglement entropy in the many-body localized regime.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Quantum Computing

Background:

  • Nonstabilizerness quantifies quantum state complexity beyond stabilizer states, crucial for quantum advantage.
  • Disordered many-body localized (MBL) systems exhibit unique quantum phenomena due to strong disorder and interactions.

Purpose of the Study:

  • Investigate the dynamics and spreading of nonstabilizerness in disordered MBL systems.
  • Understand the role of interactions in influencing nonstabilizerness.
  • Explore the relationship between nonstabilizerness and entanglement entropy in MBL systems.

Main Methods:

  • Utilized the stabilizer Rényi entropy (SRE) to quantify nonstabilizerness.
  • Employed a phenomenological ℓ-bit model for analytical insights.
  • Performed numerical simulations on the disordered transverse-field Ising model.

Main Results:

  • Demonstrated power-law growth of SRE due to interactions in MBL systems, contrasting with ergodic systems.
  • Validated theoretical predictions with numerical simulations across various parameters.
  • Discovered a universal scaling relationship between SRE and entanglement entropy in the MBL regime.

Conclusions:

  • Interactions significantly drive nonstabilizerness spreading in disordered MBL systems.
  • The MBL regime exhibits distinct nonstabilizerness dynamics compared to ergodic systems.
  • A universal connection exists between quantum complexity (nonstabilizerness) and entanglement in MBL systems.