Similarity Renormalization Group decouples the Hamiltonian band-diagonally
The SRG (Wegner 1994) uses a flow equation dH/ds = [η, H] with η = [H_d, H] to eliminate off-diagonal couplings. Off-diagonal elements H_{ij} decay as e^{−s(E_i−E_j)²}, driving H toward band-diagonal form. The color shows matrix element magnitude — watch off-diagonal strength flow to zero.