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Subsystem eigenstate thermalization hypothesis
Anatoly Dymarsky1,2, Nima Lashkari3, Hong Liu3
1Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA.
Abstract:
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.
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