Testing whether all eigenstates obey the eigenstate thermalization hypothesis

Hyungwon Kim, Tatsuhiko N. Ikeda, David A. Huse

Research output: Contribution to journalArticlepeer-review

284 Scopus citations


We ask whether the eigenstate thermalization hypothesis (ETH) is valid in a strong sense: in the limit of an infinite system, every eigenstate is thermal. We examine expectation values of few-body operators in highly excited many-body eigenstates and search for "outliers," the eigenstates that deviate the most from ETH. We use exact diagonalization of two one-dimensional nonintegrable models: a quantum Ising chain with transverse and longitudinal fields, and hard-core bosons at half-filling with nearest- and next-nearest-neighbor hopping and interaction. We show that even the most extreme outliers appear to obey ETH as the system size increases and thus provide numerical evidences that support ETH in this strong sense. Finally, periodically driving the Ising Hamiltonian, we show that the eigenstates of the corresponding Floquet operator obey ETH even more closely. We attribute this better thermalization to removing the constraint of conservation of the total energy.

Original languageEnglish (US)
Article number052105
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number5
StatePublished - Nov 6 2014

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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