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000019849 0247_ $$2DOI$$a10.1016/j.aop.2011.06.004
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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)$$aJournal Article
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000019849 440_0 $$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__ $$aThe Schrieffer-Wolff (SW) method is a version of degenerate perturbation theory in which the low-energy effective Hamiltonian Her is obtained from the exact Hamiltonian by a unitary transformation decoupling the low-energy and high-energy subspaces. We give a self-contained summary of the SW method with a focus on rigorous results. We begin with an exact definition of the SW transformation in terms of the so-called direct rotation between linear subspaces. From this we obtain elementary proofs of several important properties of H-eff such as the linked cluster theorem. We then study the perturbative version of the SW transformation obtained from a Taylor series representation of the direct rotation. Our perturbative approach provides a systematic diagram technique for computing high-order corrections to H-eff. We then specialize the SW method to quantum spin lattices with short-range interactions. We establish unitary equivalence between effective low-energy Hamiltonians obtained using two different versions of the SW method studied in the literature. Finally, we derive an upper bound on the precision up to which the ground state energy of the nth-order effective Hamiltonian approximates the exact ground state energy. (C) 2011 Elsevier Inc. All rights reserved.
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000019849 65320 $$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
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