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arXiv:2002.01857

Does the Eigenstate Thermalization Hypothesis Imply Thermalization?

Oleg Valerievich Inozemcev, Igor Vasil'evich Volovich

Published Feb 5, 2020• 0 citations
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Abstract

Eigenstate thermalization hypothesis (ETH) is discussed. We show that one common formulation of ETH does not necessarily imply thermalization of an observable of isolated many body quantum system. To get thermalization one has to postulate the canonical or microcanonical distribution in the ETH-ansatz. More generally, any other average can be postulated in the generalized ETH-ansatz which leads to a corresponding equilibration condition.

DOI
10.48550/arxiv.2002.01857

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Eigenstate thermalization hypothesis (ETH) is discussed. We show that one common formulation of ETH does not necessarily imply thermalization of an observable of isolated many body quantum system. To get thermalization one has to postulate the canonical or microcanonical distribution in the ETH-ansatz. More generally, any other average can be postulated in the generalized ETH-ansatz which leads to a corresponding equilibration condition.
The eigenstate thermalization hypothesis (ETH) explains why nonintegrable 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 operators' time-averaged and thermal expectation values. In many cases, we prove, the time average thermalizes. However, we 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.