%0 Journal Article %J Phys. Rev. Lett. %D 2023 %T Non-Abelian eigenstate thermalization hypothesis %A Murthy, Chaitanya %A Babakhani, Arman %A Iniguez, Fernando %A Srednicki, Mark %A Nicole Yunger Halpern %K FOS: Physical sciences %K High Energy Physics - Theory (hep-th) %K Quantum Gases (cond-mat.quant-gas) %K Quantum Physics (quant-ph) %K Statistical Mechanics (cond-mat.stat-mech) %K Strongly Correlated Electrons (cond-mat.str-el) %X

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' 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.

%B Phys. Rev. Lett. %V 130 %8 4/6/2023 %G eng %U https://arxiv.org/abs/2206.05310 %& 140402 %R https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.140402