Eigenstate thermalization hypothesis through the lens of autocorrelation functions

Article

关键词: STATISTICAL-MECHANICS;    QUANTUM;    CHAOS;    ENTANGLEMENT;    EQUILIBRIUM;    RELAXATION;   

DOI  :  10.1103/PhysRevB.103.235137

来源: SCIE

【 摘 要 】

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 vertical bar vertical bar(2) in the limit of small eigenstate energy differences omega = E-beta - E-alpha. Removing the dominant exponential suppression of vertical bar vertical bar(2), we find that (1) the current matrix elements exhibit a system-size dependence that is different from other observables under investigation and (2) 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.

【 授权许可】

Free