Eigenstate thermalization hypothesis through the lens of autocorrelation functions

• URL: http://arxiv.org/abs/2011.13958v3
• Date: Sat, 25 Sep 2021 10:47:54 GMT
• Title: Eigenstate thermalization hypothesis through the lens of autocorrelation functions
• Authors: C. Sch\"onle, D. Jansen, F. Heidrich-Meisner, L. Vidmar
• Abstract summary: Matrix elements of observables in eigenstates of generic Hamiltonians are described by the Srednicki ansatz. We study a quantum chaotic spin-fermion model in a one-dimensional lattice.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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