We investigate the time dependence of anti-flatness in the entanglement spectrum, a measure for non-stabilizerness and lower bound for non-local quantum magic, on a subsystem of a linear SU(2) plaquette chain during thermalization. Tracing the time evolution of a large number of initial states, we find that the anti-flatness exhibits a barrier-like maximum during the time period when the entanglement entropy of the subsystem grows rapidly from the initial value to the microcanonical entropy. The location of the peak is strongly correlated with the time when the entanglement exhibits the strongest growth. This behavior is found for generic highly excited initial computational basis states and persists for coupling constants across the ergodic regime, revealing a universal structure of the entanglement spectrum during thermalization. We conclude that quantitative simulations of thermalization for nonabelian gauge theories require quantum computing. We speculate that this property generalizes to other quantum chaotic systems.
The authors gratefully acknowledge the scientific support and HPC resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universita ̈t Erlangen-Nu ̈rnberg(FAU).B.M.acknowledgessupport by the U.S. Department of Energy, Office of Science (grant DE-FG02-05ER41367). X.Y. is supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, InQubator for Quantum Simulation (IQuS) (https://iqus.uw.edu) under Award Number DOE (NP) Award DE-SC0020970 via the program on Quantum Horizons: QIS Research and Innovation for Nuclear Science and acknowledges the discussions at the “Many-Body Quantum Magic” workshop held at the IQuS hosted by the Institute for Nuclear Theory in Spring 2025. L.E. acknowledges funding by the Max Planck Society, the Deutsche Forschungsgemein- schaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2111 – 390814868, and the European Research Council (ERC) under the European Union’s Horizon Europe research and innovation program (Grant Agreement No. 101165667)—ERC Starting Grant QuSiGauge. Views and opinions expressed are those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. This work is part of the Quantum Computing for High-Energy Physics (QC4HEP) working group. C.S. would like to thank the organizers and participants of the QuantHEP 2025 conference at Lawrence Berkeley National Lab for valuable discussions that contributed to this work.
