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@ARTICLE{Bravyi:19849,
      author       = {Bravyi, S. and DiVincenzo, D.P. and Loss, D.},
      title        = {{S}chrieffer-{W}olff transformation for quantum many-body
                      systems},
      journal      = {Annals of physics},
      volume       = {326},
      issn         = {0003-4916},
      address      = {Amsterdam [u.a.]},
      publisher    = {Elsevier},
      reportid     = {PreJuSER-19849},
      pages        = {2793 - 2826},
      year         = {2011},
      note         = {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.},
      abstract     = {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.},
      keywords     = {J (WoSType)},
      cin          = {PGI-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-2-20110106},
      pnm          = {Grundlagen für zukünftige Informationstechnologien},
      pid          = {G:(DE-Juel1)FUEK412},
      shelfmark    = {Physics, Multidisciplinary},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000295345300011},
      doi          = {10.1016/j.aop.2011.06.004},
      url          = {https://juser.fz-juelich.de/record/19849},
}