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Physica A Statistical Mechanics and its Applications

On the time evolution of large systems: A soluble model with two-body interactions

Hans Jürgen Kreuzer, ANTON Z. CAPRI

Published Jan 1, 1975• 5 citations
Publisher
DOI
10.1016/0378-4371(75)90056-4

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Out-of-time-ordered correlators (OTOCs) describe information scrambling under unitary time evolution, and provide a useful probe of the emergence of quantum chaos. Here we calculate OTOCs for a model of disorder-free localization whose exact solubility allows us to study long-time behavior in large systems. Remarkably, we observe logarithmic spreading of correlations, qualitatively different to both thermalizing and Anderson localized systems. Rather, such behavior is normally taken as a signature of many-body localization, so that our findings for an essentially noninteracting model are surprising. We provide an explanation for this unusual behavior, and suggest a novel Loschmidt echo protocol as a probe of correlation spreading. We show that the logarithmic spreading of correlations probed by this protocol is a generic feature of localized systems, with or without interactions.
We present a formal derivation of the exact dynamics of the one-body density matrix. Its essential ingredients are shown to be the following: (a) a mean field unitary time evolution; (b) irreducible nonunitary corrections to the unitary evolution (collision effects); and (c) effects due to the time evolution of initial state correlation [which contribute to both (a) and (b)]. In the weak coupling limit the collision effects give rise to a term of Boltzmann form. A qualitative discussion of the importance of collision effects for the expectation values of one-body operators and a quantitative illustration in the framework of an exactly soluble model are given. In this case one finds large nonunitary contributions.NUCLEAR STRUCTURE Exact microscopic description of the time evolution of the one body density matrix.