Non-stabilizerness and U(1) symmetry in chaotic many-body quantum systems

• URL: http://arxiv.org/abs/2603.28870v1
• Date: Mon, 30 Mar 2026 18:00:10 GMT
• Title: Non-stabilizerness and U(1) symmetry in chaotic many-body quantum systems
• Abstract summary: We show that the presence of a conserved charge leads to a substantial suppression of non-stabilizerness (magic) compared to the unconstrained case.<n>In the thermodynamic limit, stabilizer entropy exhibits a different leading-order scaling close to a vanishing relative charge density.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present exact, closed-form results for the non-stabilizerness of random pure states subject to a U(1) symmetry constraint. Using stabilizer entropy as our non-stabilizerness monotone, we derive the average and the variance for U(1)-constrained Haar random states. We show that the presence of a conserved charge leads to a substantial suppression of non-stabilizerness (magic) compared to the unconstrained case, and identify a qualitative difference between entanglement and magic response. In the thermodynamic limit, stabilizer entropy exhibits a different leading-order scaling close to a vanishing relative charge density, implying that magic is more robust to charge density fluctuations than entanglement entropy. We test our analytical predictions against midspectrum eigenstates of two chaotic many-body systems with conserved $U(1)$ charge: the complex-fermion Sachdev-Ye-Kitaev (cSYK) model and a Heisenberg XXZ chain with next-to-nearest-neighbour couplings and conserved magnetization. We find an excellent agreement for the non-local cSYK model and systematic deviations for the local XXZ chain, highlighting the role of interaction locality.

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