000019849 001__ 19849 000019849 005__ 20190625111858.0 000019849 0247_ $$2DOI$$a10.1016/j.aop.2011.06.004 000019849 0247_ $$2WOS$$aWOS:000295345300011 000019849 0247_ $$2altmetric$$aaltmetric:3654571 000019849 037__ $$aPreJuSER-19849 000019849 041__ $$aeng 000019849 082__ $$a530 000019849 084__ $$2WoS$$aPhysics, Multidisciplinary 000019849 1001_ $$0P:(DE-HGF)0$$aBravyi, S.$$b0 000019849 245__ $$aSchrieffer-Wolff transformation for quantum many-body systems 000019849 260__ $$aAmsterdam [u.a.]$$bElsevier$$c2011 000019849 300__ $$a2793 - 2826 000019849 3367_ $$0PUB:(DE-HGF)16$$2PUB:(DE-HGF)$$aJournal Article 000019849 3367_ $$2DataCite$$aOutput Types/Journal article 000019849 3367_ $$00$$2EndNote$$aJournal Article 000019849 3367_ $$2BibTeX$$aARTICLE 000019849 3367_ $$2ORCID$$aJOURNAL_ARTICLE 000019849 3367_ $$2DRIVER$$aarticle 000019849 440_0 $$08601$$aAnnals of Physics$$v326$$x0003-4916$$y10 000019849 500__ $$3POF3_Assignment on 2016-02-29 000019849 500__ $$aWe 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. 000019849 520__ $$aThe Schrieffer-Wolff (SW) method is a version of degenerate perturbation theory in which the low-energy effective Hamiltonian Her is obtained from the exact Hamiltonian by a unitary transformation decoupling the low-energy and high-energy subspaces. We give a self-contained summary of the SW method with a focus on rigorous results. We begin with an exact definition of the SW transformation in terms of the so-called direct rotation between linear subspaces. From this we obtain elementary proofs of several important properties of H-eff such as the linked cluster theorem. We then study the perturbative version of the SW transformation obtained from a Taylor series representation of the direct rotation. Our perturbative approach provides a systematic diagram technique for computing high-order corrections to H-eff. We then specialize the SW method to quantum spin lattices with short-range interactions. We establish unitary equivalence between effective low-energy Hamiltonians obtained using two different versions of the SW method studied in the literature. Finally, we derive an upper bound on the precision up to which the ground state energy of the nth-order effective Hamiltonian approximates the exact ground state energy. (C) 2011 Elsevier Inc. All rights reserved. 000019849 536__ $$0G:(DE-Juel1)FUEK412$$2G:(DE-HGF)$$aGrundlagen für zukünftige Informationstechnologien$$cP42$$x0 000019849 588__ $$aDataset connected to Web of Science 000019849 65320 $$2Author$$aQuantum many-body system 000019849 65320 $$2Author$$aPerturbative expansion 000019849 65320 $$2Author$$aCanonical transformation 000019849 650_7 $$2WoSType$$aJ 000019849 7001_ $$0P:(DE-Juel1)143759$$aDiVincenzo, D.P.$$b1$$uFZJ 000019849 7001_ $$0P:(DE-HGF)0$$aLoss, D.$$b2 000019849 773__ $$0PERI:(DE-600)1461336-0$$a10.1016/j.aop.2011.06.004$$gVol. 326, p. 2793 - 2826$$p2793 - 2826$$q326<2793 - 2826$$tAnnals of physics$$v326$$x0003-4916$$y2011 000019849 909CO $$ooai:juser.fz-juelich.de:19849$$pVDB 000019849 915__ $$0StatID:(DE-HGF)0010$$aJCR/ISI refereed 000019849 9141_ $$y2011 000019849 9131_ $$0G:(DE-Juel1)FUEK412$$aDE-HGF$$bSchlüsseltechnologien$$kP42$$lGrundlagen für zukünftige Informationstechnologien (FIT)$$vGrundlagen für zukünftige Informationstechnologien$$x0 000019849 9132_ $$0G:(DE-HGF)POF3-529H$$1G:(DE-HGF)POF3-520$$2G:(DE-HGF)POF3-500$$aDE-HGF$$bKey Technologies$$lFuture Information Technology - Fundamentals, Novel Concepts and Energy Efficiency (FIT)$$vAddenda$$x0 000019849 9201_ $$0I:(DE-Juel1)PGI-2-20110106$$gPGI$$kPGI-2$$lTheoretische Nanoelektronik$$x0 000019849 970__ $$aVDB:(DE-Juel1)134862 000019849 980__ $$aVDB 000019849 980__ $$aConvertedRecord 000019849 980__ $$ajournal 000019849 980__ $$aI:(DE-Juel1)PGI-2-20110106 000019849 980__ $$aUNRESTRICTED