 Sergey Bravyi

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.^[ref]

For a Quantum Hamiltonian $H$, an anti-Hermitian generator $S$ gives $H_{\mathrm{eff}}=P{e}^{S}H{e}^{-S}P$ 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.