Thermalization speed with noncommuting conserved charges
In plain words
Standard thermalization theory assumes all conserved quantities (energy, particle number) can be measured at once. When some cannot, for example the three components of total spin, it is unclear whether thermalization works the same way and at the same speed.
Precise statement
For a chaotic local Hamiltonian with $\mathrm{SU}(2)$ symmetry (e.g. a spin-1/2 Heisenberg chain with next-nearest-neighbour exchange $J_2$), the non-Abelian ETH (Murthy, Babakhani, Iniguez, Srednicki, Yunger Halpern, PRL 130, 140402, 2023) predicts thermalization of time averages, with identified cases where the approach to the thermal value is anomalously slow in system size $N$. Determine the scaling with N of the deviation of long-time averages of local observables from the non-Abelian thermal state, compared with $\sim 1/N$ for commuting charges, and whether the slow cases persist as $N \to \infty$. Answer: the scaling law.
What would settle it
Exact diagonalization resolved by SU(2) multiplet up to the largest accessible N, combined with an analytic estimate from the Clebsch-Gordan structure of local operators.
Status in the literature
Non-Abelian ETH was proposed in 2023; the size scaling of the slow cases is not established (moderate confidence).