The eigenstate thermalization hypothesis (ETH) explains why chaotic quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. If the Hamiltonian conserves one quantity (\"charge\"), the ETH implies thermalization within a charge sector -- in a microcanonical subspace. But quantum systems can have charges that fail to commute with each other and so share no eigenbasis; microcanonical subspaces may not exist. Furthermore, the Hamiltonian will have degeneracies, so the ETH need not imply thermalization. We adapt the ETH to noncommuting charges by positing a non-Abelian ETH and invoking the approximate microcanonical subspace introduced in quantum thermodynamics. Illustrating with SU(2) symmetry, we apply the non-Abelian ETH in calculating local observables\&$\#$39; time-averaged and thermal expectation values. In many cases, we prove, the time average thermalizes. However, we also find cases in which, under a physically reasonable assumption, the time average converges to the thermal average unusually slowly as a function of the global-system size. This work extends the ETH, a cornerstone of many-body physics, to noncommuting charges, recently a subject of intense activity in quantum thermodynamics.

}, keywords = {FOS: Physical sciences, High Energy Physics - Theory (hep-th), Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph), Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2206.05310}, url = {https://arxiv.org/abs/2206.05310}, author = {Murthy, Chaitanya and Babakhani, Arman and Iniguez, Fernando and Srednicki, Mark and Nicole Yunger Halpern} }