The exact solution of the above Hamiltonian using the complete Hilbert space is already intractable for more than N = 10 ∼ 20 molecules. This is because the dimension of the Hamiltonian scales exponentially with the number of molecules as dim[ ĤTC ] ∝ 2 N assuming that the molecular degrees of freedom (DOFs) have only two basis states, {|g⟩, |e⟩}. However, since we are interested in collective effects, we will restrict the description of the above Hamiltonian to the basis of the first-excited subspace. In the singly excited subspace, the dimension scales as dim[ ĤTC ] ∝ N .