Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians

P. Łydżba,1 Yicheng Zhang,2 Marcos Rigol,2 Lev Vidmar3,4

1Department of Theoretical Physics, Wroclaw University of Science and Technology, 50-370 Wrocław, Poland

2Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA

3Department f Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia

4Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia

In this presentation, we study single-particle properties of quantum-chaotic quadratic models, which are identified with quadratic models having random matrix theory correlations in single-particle spectra, i.e., exhibiting single-particle quantum chaos. We analyze matrix elements of local and nonlocal operators in two paradigmatic Hamiltonians, i.e., the quadratic Sachdev-Ye-Kitaev model and the three-dimensional Anderson model below the localization transition. We demonstrate that their matrix elements display single-particle eigenstate thermalization. Specifically, we show that the diagonal matrix elements exhibit vanishing eigenstate-to-eigenstate fluctuations, and the variance proportional to the inverse Hilbert space dimension. We also demonstrate that the ratio between the variance of diagonal and off-diagonal matrix elements agrees with the prediction of random matrix theory. We also study distributions of matrix elements, and establish the conditions under which they are (not) Gaussian.

1. P. Łydżba et al. Phys. Rev. Lett. 125, 180604 (2020)
2. P. Łydżba et al. Phys. Rev. B 103, 104206 (2021)
3. P. Łydżba et al. arXiv:2109.06895 (2021)

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