where the n th exciton has site energy of ε n and the exciton is coupled to the cavity mode of energy ℏω c with a light-matter coupling strength of ℏg n c . Here, σ † n = |e n ⟩⟨g n | and σn = |g n ⟩⟨e n | creates and annilates an excitation on the n th molecule, respectively, with |g n ⟩ and |e n ⟩ as the ground and excited states for molecule n. Additionally, each exciton site is also coupled to a set of harmonic bath coordinates ν, which are described by the bath Hamiltonian,