Microscopic justification of the eigenstate thermalization hypothesis (ETH)

The ETH explains how isolated quantum many-body systems thermalize by proposing that each energy eigenstate is already thermal [1]. ETH has been shown to be essential to the understanding of quantum chaos and implies various important thermodynamic relations [2].
While by now there are many numerical verifications of ETH, only few analytical arguments for its validity have been found. One such analytical argument is based on a semiclassical limit [3]. Another important argument was given by Deutsch who showed how a small interaction which is modelled by a random matrix leads to ETH [4].
Our work adopts this idea and analyzes whether a generic quantum system can be treated as a random matrix. To do this we employ continuous unitary transformations to map an initial Hamiltonian to an effective one. This effective Hamiltonian turns out to have a simple banded form and can be compared to a random matrix. By studying its statistical properties we are able to use the analytical flow equation approach to close the gap in Deutsch's reasoning. Our results depict a first step towards a microscopic justification of ETH.

[1] M. Rigol et al., Nature 452 (2008)
[2] L. D'Alessio et al., Adv. in Phys. Vol. 65 (2016)
[3] M. Srednicki, Phys. Rev. E 50 (1994)
[4] J.M. Deutsch, Phys. Rev. A 43 (1991)