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001     19849
005     20190625111858.0
024 7 _ |2 DOI
|a 10.1016/j.aop.2011.06.004
024 7 _ |2 WOS
|a WOS:000295345300011
024 7 _ |a altmetric:3654571
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037 _ _ |a PreJuSER-19849
041 _ _ |a eng
082 _ _ |a 530
084 _ _ |2 WoS
|a Physics, Multidisciplinary
100 1 _ |0 P:(DE-HGF)0
|a Bravyi, S.
|b 0
245 _ _ |a Schrieffer-Wolff transformation for quantum many-body systems
260 _ _ |a Amsterdam [u.a.]
|b Elsevier
|c 2011
300 _ _ |a 2793 - 2826
336 7 _ |a Journal Article
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336 7 _ |a ARTICLE
|2 BibTeX
336 7 _ |a JOURNAL_ARTICLE
|2 ORCID
336 7 _ |a article
|2 DRIVER
440 _ 0 |0 8601
|a Annals of Physics
|v 326
|x 0003-4916
|y 10
500 _ _ |3 POF3_Assignment on 2016-02-29
500 _ _ |a We thank Barbara Terhal for useful discussions. SB would like to thank RWTH Aachen University and the University of Basel for hospitality during several stages of this work. SB was partially supported by the DARPA QuEST program under contract number HR0011-09-C-0047. DL was partially supported by the Swiss NSF, NCCR Nanoscience, NCCR QSIT, and DARPA QuEST.
520 _ _ |a The Schrieffer-Wolff (SW) method is a version of degenerate perturbation theory in which the low-energy effective Hamiltonian Her is obtained from the exact Hamiltonian by a unitary transformation decoupling the low-energy and high-energy subspaces. We give a self-contained summary of the SW method with a focus on rigorous results. We begin with an exact definition of the SW transformation in terms of the so-called direct rotation between linear subspaces. From this we obtain elementary proofs of several important properties of H-eff such as the linked cluster theorem. We then study the perturbative version of the SW transformation obtained from a Taylor series representation of the direct rotation. Our perturbative approach provides a systematic diagram technique for computing high-order corrections to H-eff. We then specialize the SW method to quantum spin lattices with short-range interactions. We establish unitary equivalence between effective low-energy Hamiltonians obtained using two different versions of the SW method studied in the literature. Finally, we derive an upper bound on the precision up to which the ground state energy of the nth-order effective Hamiltonian approximates the exact ground state energy. (C) 2011 Elsevier Inc. All rights reserved.
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650 _ 7 |2 WoSType
|a J
653 2 0 |2 Author
|a Quantum many-body system
653 2 0 |2 Author
|a Perturbative expansion
653 2 0 |2 Author
|a Canonical transformation
700 1 _ |0 P:(DE-Juel1)143759
|a DiVincenzo, D.P.
|b 1
|u FZJ
700 1 _ |0 P:(DE-HGF)0
|a Loss, D.
|b 2
773 _ _ |0 PERI:(DE-600)1461336-0
|a 10.1016/j.aop.2011.06.004
|g Vol. 326, p. 2793 - 2826
|p 2793 - 2826
|q 326<2793 - 2826
|t Annals of physics
|v 326
|x 0003-4916
|y 2011
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914 1 _ |y 2011
915 _ _ |0 StatID:(DE-HGF)0010
|a JCR/ISI refereed
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|l Theoretische Nanoelektronik
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