Non-Abelian eigenstate thermalization hypothesis

• URL: http://arxiv.org/abs/2206.05310v2
• Date: Fri, 21 Apr 2023 17:27:33 GMT
• Title: Non-Abelian eigenstate thermalization hypothesis
• Authors: Chaitanya Murthy, Arman Babakhani, Fernando Iniguez, Mark Srednicki, Nicole Yunger Halpern
• Abstract summary: The eigenstate thermalization hypothesis (ETH) explains why chaotic quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. We adapt the ETH to noncommuting charges by positing a non-Abelian ETH and invoking the approximate microcanonical subspace introduced in quantum thermodynamics.
• Score: 58.720142291102135
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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