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Testing whether all eigenstates obey the eigenstate thermalization hypothesis

Author(s): Kim, Hyungwon; Ikeda, Tatsuhiko N; Huse, David A

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Abstract: 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.
Publication Date: Nov-2014
Electronic Publication Date: 6-Nov-2014
Citation: Kim, Hyungwon, Ikeda, Tatsuhiko N, Huse, David A. (2014). Testing whether all eigenstates obey the eigenstate thermalization hypothesis. Physical Review E, 90 (5), 10.1103/PhysRevE.90.052105
DOI: doi:10.1103/PhysRevE.90.052105
ISSN: 1539-3755
EISSN: 1550-2376
Type of Material: Journal Article
Journal/Proceeding Title: Physical Review E
Version: Author's manuscript

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