Regression relation for pure quantum states and its implications for efficient computing

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dc.AffiliationOctober University for modern sciences and Arts (MSA)
dc.contributor.authorA. Elsayed, Tarek
dc.contributor.authorV. Fine, Boris
dc.date.accessioned2020-02-26T07:06:49Z
dc.date.available2020-02-26T07:06:49Z
dc.date.issued2013
dc.descriptionMSA Google Scholaren_US
dc.description.abstractWe obtain a modified version of the Onsager regression relation for the expectation values of quantum-mechanical operators in pure quantum states of isolated many-body quantum systems. We use the insights gained from this relation to show that high-temperature time correlation functions in many-body quantum systems can be controllably computed without complete diagonalization of the Hamiltonians, using instead the direct integration of the Schroedinger equation for randomly sampled pure states. This method is also applicable to quantum quenches and other situations describable by time-dependent many-body Hamiltonians. The method implies exponential reduction of the computer memory requirement in comparison with the complete diagonalization. We illustrate the method by numerically computing infinite-temperature correlation functions for translationally invariant Heisenberg chains of up to 29 spins 1/2. Thereby, we also test the spin diffusion hypothesis and find it in a satisfactory agreement with the numerical results. Both the derivation of the modified regression relation and the justification of the computational method are based on the notion of quantum typicality.en_US
dc.description.sponsorshipAmerican Physical Societyen_US
dc.description.urihttps://www.scimagojr.com/journalsearch.php?q=29150&tip=sid&clean=0
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dc.identifier.urihttps://t.ly/zNBmp
dc.language.isoenen_US
dc.publisherAmerican Physical Societyen_US
dc.relation.ispartofseriesPhysical review letters;Volume: 110 Issue: 7 Pages: 1-16
dc.subjectUniversity of Pure quantum statesen_US
dc.titleRegression relation for pure quantum states and its implications for efficient computingen_US
dc.typeArticleen_US

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