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arXiv · 2011.13958

Eigenstate thermalization hypothesis through the lens of autocorrelation functions

C. Schönle·D. Jansen·F. Heidrich-Meisner·L. Vidmar
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Abstract

Matrix elements of observables in eigenstates of generic Hamiltonians are described by the Srednicki ansatz within the eigenstate thermalization hypothesis (ETH). We study a quantum chaotic spin-fermion model in a one-dimensional lattice, which consists of a spin-1/2 XX chain coupled to a single itinerant fermion. In our study, we focus on translationally invariant observables including the charge and energy current, thereby also connecting the ETH with transport properties. Considering observables with a Hilbert-Schmidt norm of one, we first perform a comprehensive analysis of ETH in the model taking into account latest developments. A particular emphasis is on the analysis of the structure of the offdiagonal matrix elements $|\langle \alpha | \hat O | \beta \rangle|^2$ in the limit of small eigenstate energy differences $\omega = E_\beta - E_\alpha$. Removing the dominant exponential suppression of $|\langle \alpha | \hat O | \beta \rangle|^2$, we find that: (i) the current matrix elements exhibit a system-size dependence that is different from other observables under investigation, (ii) matrix elements of several other observables exhibit a Drude-like structure with a Lorentzian frequency dependence. We then show how this information can be extracted from the autocorrelation functions as well. Finally, our study is complemented by a numerical analysis of the fluctuation-dissipation relation for eigenstates in the bulk of the spectrum. We identify the regime of $\omega$ in which the well-known fluctuation-dissipation relation is valid with high accuracy for finite systems.

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BibTeXRIS

C. Schönle, D. Jansen, F. Heidrich-Meisner, L. Vidmar. 2020-11-27. Eigenstate thermalization hypothesis through the lens of autocorrelation functions. https://doi.org/10.1103/physrevb.103.235137

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