Motivated by the qualitative picture of canonical typicality, we propose a refined formulation of the eigenstate thermalization hypothesis (ETH) for chaotic quantum systems. This formulation, which we refer to as subsystem ETH, is in terms of the reduced density matrix of subsystems. This strong form of ETH outlines the set of observables defined within the subsystem for which it guarantees eigenstate thermalization. We discuss the limits when the size of the subsystem is small or comparable to its complement. In the latter case we outline the way to calculate the leading volume-proportional contribution to the von Neumann and Renyi entanglment entropies. Finally, we provide numerical evidence for the proposal in the case of a one-dimensional Ising spin chain.
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|State||Published - Jan 25 2018|
Bibliographical noteFunding Information:
This work was supported by funds provided by MIT-Skoltech Initiative. We would like to thank the University of Kentucky Center for Computational Sciences for computing time on the Lipscomb High Performance Computing Cluster.
© 2018 American Physical Society.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics