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

TL;DR

This paper derives exact formulas for non-stabilizerness in U(1)-constrained random states, showing charge conservation suppresses magic and affects its scaling compared to entanglement, with tests on chaotic many-body systems.

Contribution

It provides analytical results for stabilizer entropy under U(1) symmetry and compares predictions with numerical data from chaotic models.

Findings

Charge conservation suppresses non-stabilizerness compared to unconstrained states.

Stabilizer entropy scales differently near zero charge density, indicating robustness to charge fluctuations.

Excellent agreement with cSYK model; deviations observed in local XXZ chain due to interaction locality.

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.