Eigenstate thermalization hypothesis through the lens of autocorrelation functions
| Autor: | Christoph Schönle, Fabian Heidrich-Meisner, David Jansen, Lev Vidmar |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Quantum Physics Statistical Mechanics (cond-mat.stat-mech) Strongly Correlated Electrons (cond-mat.str-el) FOS: Physical sciences Observable 02 engineering and technology Fermion 021001 nanoscience & nanotechnology 01 natural sciences Omega Condensed Matter - Strongly Correlated Electrons Lattice (order) 0103 physical sciences Quantum Physics (quant-ph) 010306 general physics 0210 nano-technology Eigenstate thermalization hypothesis Quantum Condensed Matter - Statistical Mechanics Eigenvalues and eigenvectors Ansatz Mathematical physics |
| Zdroj: | Physical Review B. 103 |
| ISSN: | 2469-9969 2469-9950 |
| DOI: | 10.1103/physrevb.103.235137 |
| Popis: | 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 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|