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Replica resummation of the Baker-Campbell-Hausdorff series
ID Vajna, Szabolcs (Author), ID Klobas, Katja (Author), ID Prosen, Tomaž (Author), ID Polkovnikov, Anatoli (Author)

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Abstract
We developed a novel perturbative expansion based on the replica trick for the Floquet Hamiltonian governing the dynamics of periodically kicked systems where the kick strength is the small parameter. The expansion is formally equivalent to an infinite resummation of the Baker-Campbell-Hausdorff series in the un-driven (nonperturbed) Hamiltonian, while considering terms up to a finite order in the kick strength. As an application of the replica expansion, we analyze an Ising spin 1/2 chain periodically kicked with magnetic field of strength h, which has both longitudinal and transverse components. We demonstrate that even away from the regime of high frequency driving, the heating rate is nonperturbative in the kick strength bounded from above by a stretched exponential: $e^{-\rm{const}h^{-1/2}}$. This guarantees existence of a very long pre-thermal regime, where the dynamics is governed by the Floquet Hamiltonian obtained from the replica expansion.

Language:English
Keywords:quantum mechanics, statistical physics, algebra
Typology:1.01 - Original Scientific Article
Organization:FMF - Faculty of Mathematics and Physics
Publication status:Published
Publication version:Author Accepted Manuscript
Year:2018
Number of pages:Str. 200607-1-200607-6
Numbering:Vol. 120, iss. 20
PID:20.500.12556/RUL-101523 This link opens in a new window
UDC:530.145
ISSN on article:0031-9007
DOI:10.1103/PhysRevLett.120.200607 This link opens in a new window
COBISS.SI-ID:3208292 This link opens in a new window
Publication date in RUL:13.06.2018
Views:1765
Downloads:649
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Record is a part of a journal

Title:Physical review letters
Shortened title:Phys. rev. lett.
Publisher:American Physical Society
ISSN:0031-9007
COBISS.SI-ID:1282575 This link opens in a new window

Secondary language

Language:Slovenian
Keywords:kvantna mehanika, statistična fizika, algebra

Projects

Funder:EC - European Commission
Funding programme:H2020
Project number:694544
Name:Open many-body non-equilibrium systems
Acronym:OMNES

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