Dynamical spectral weight transfer in the orbital Hatsugai-Kohmoto model

The shift in the spectral weight distribution under doping is termed the spectral weight transfer (SWT) and is a key indicator of strongly correlated physics. The static SWT ($t=0$) for doping fraction $x$ scales as $x$ for semiconductors and as $2x$ for Mott insulators. The SWT receives corrections in $t/U$ due to the noncommutativity of the kinetic and interaction terms in the Hamiltonian, termed the dynamic SWT. We compute explicitly the low-energy spectral weight (LESW) in the lower Hubbard band using the orbital Hatsugai-Kohmoto (OHK) model. We show that the dynamical mixing enters the LESW with a universal slope independent of the number of orbitals. This independence on orbital number corroborates the rapid convergence of the OHK model to the Hubbard model. As a result, OHK is an effective simulator of Hubbard physics.