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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
Summary
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.
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.
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