where Pn,ν and Rn,ν are the momentum and position operator of the ν th phonon on n th matter site of frequency ω n,ν , and 1s = 1ex ⊗ 1ph is the identity operator of the "system" subspace that includes the excitonic and photonic DOF. These bath DOF are coupled bi-linearly to the excitonic sites providing diagonal fluctuations to onsite energies