تقرير
Eigenstate thermalization hypothesis through the lens of autocorrelation functions
| العنوان: | Eigenstate thermalization hypothesis through the lens of autocorrelation functions |
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| المؤلفون: | Schönle, C., Jansen, D., Heidrich-Meisner, F., Vidmar, L. |
| المصدر: | Phys. Rev. B 103, 235137 (2021) |
| سنة النشر: | 2020 |
| المجموعة: | Condensed Matter Quantum Physics |
| مصطلحات موضوعية: | Condensed Matter - Statistical Mechanics, Condensed Matter - Strongly Correlated Electrons, Quantum Physics |
| الوصف: | 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. Comment: v3: Data shown in figures now available as ancillary files |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevB.103.235137 |
| URL الوصول: | http://arxiv.org/abs/2011.13958 |
| رقم الأكسشن: | edsarx.2011.13958 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevB.103.235137 |
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