Abstract
Having analytical instances of the eigenstate thermalization hypothesis (ETH) is of obvious interest, both for fundamental and applied reasons. This is generally a hard task, due to the belief that nonlinear interactions are basic ingredients of the thermalization mechanism. In this article we prove that random Gaussian-free fermions satisfy ETH in the multiparticle sector, by analytically computing the correlations and entanglement entropies of the theory. With the explicit construction at hand, we finally comment on the differences between fully random Hamiltonians and random Gaussian systems, providing a physically motivated notion of randomness of the microscopic quantum state.
| Original language | English |
|---|---|
| Article number | 030401 |
| Number of pages | 5 |
| Journal | Physical Review Letters |
| Volume | 116 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 22 Jan 2016 |
Funding
It is a pleasure to thank Jose Barbon, Marcos Crichigno, Simone Paganelli, and Stefan Vandoren for interesting discussions in closely related subjects, Hrachya Babujian for useful comments on the manuscript, and the constructive criticisms of an anonymous referee. The author also wishes to thank all the participants of the workshop "Strongly coupled field theories for condensed matter and quantum information," held in Natal, Brazil, in which this work was presented, and especially the hospitality of the International Institute of Physics, located in Natal, in which part of this work was developed. This work was supported by the Delta-Institute for Theoretical Physics (D-ITP) that is funded by the Dutch Ministry of Education, Culture and Science (OCW).
Keywords
- RANDOM-MATRIX THEORY
- STATISTICAL-MECHANICS
- CHAOS