Anomalous Thermalization in Ergodic Systems

David J. Luitz, Yevgeny Bar Lev

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133 Scopus citations


It is commonly believed that quantum isolated systems satisfying the eigenstate thermalization hypothesis (ETH) are diffusive. We show that this assumption is too restrictive since there are systems that are asymptotically in a thermal state yet exhibit anomalous, subdiffusive thermalization. We show that such systems satisfy a modified version of the ETH ansatz and derive a general connection between the scaling of the variance of the off-diagonal matrix elements of local operators, written in the eigenbasis of the Hamiltonian, and the dynamical exponent. We find that for subdiffusively thermalizing systems the variance scales more slowly with system size than expected for diffusive systems. We corroborate our findings by numerically studying the distribution of the coefficients of the eigenfunctions and the off-diagonal matrix elements of local operators of the random field Heisenberg chain, which has anomalous transport in its thermal phase. Surprisingly, this system also has non-Gaussian distributions of the eigenfunctions, thus, directly violating Berry's conjecture.

Original languageEnglish
Article number170404
JournalPhysical Review Letters
Issue number17
StatePublished - 21 Oct 2016
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy


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