= Sergey Bravyi
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<Sergey Bravyi> developed rigorous treatments of the <Schrieffer-Wolff transformation> with <David DiVincenzo> and <Daniel Loss>. Their 2011 work derives low-energy effective quantum dynamics through a <unitary transformation> that decouples low- and high-energy subspaces.<Schrieffer-Wolff transformation for quantum many-body systems by Sergey Bravyi and others>[Abstract: exact direct rotation, perturbative expansion and error bounds]{ref}
For a <Quantum Hamiltonian> $H$, an anti-Hermitian generator $S$ gives $H_{\rm eff}=P e^SHe^{-S}P$ with $P$ the <orthogonal projection> onto the chosen low-energy subspace, when the transformation is constructed appropriately. Bounding the approximation matters: formally discarding high-energy states without controlling their virtual coupling can miss low-energy corrections.
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