Eigenstate thermalization hypothesis through the lens of autocorrelation functions

摘要: Matrix elements of observables in eigenstates generic Hamiltonians are described by the Srednicki ansatz within eigenstate thermalization hypothesis (ETH). We study a quantum chaotic spin-fermion model one-dimensional lattice, which consists spin-1/2 XX chain coupled to single itinerant fermion. In our study, we focus on translationally invariant including charge and energy current, thereby also connecting ETH with transport properties. ask extent one can use autocorrelation functions extract specific properties their matrix elements. Considering Hilbert-Schmidt norm one, first demonstrate validity remarkable accuracy. A particular emphasis is analysis structure offdiagonal $|\langle \alpha | \hat O \beta \rangle|^2$ limit small differences $\omega = E_\beta - E_\alpha$. Removing dominant exponential suppression \rangle|^2$, find that: (i) current elements, contrast all other under investigation, exhibit no additional system-size dependence, (ii) several Drude-like Lorentzian frequency whose amplitude width scales linearly lattice size, eventually suggesting ballistic for large systems. then show how this information be extracted from as well. Finally, complemented numerical fluctuation-dissipation relation bulk spectrum. identify regime $\omega$ well-known valid high accuracy finite