since V ± = 0, V ±,∓ = ∆/2, and there are no nuclear DOFs. As discussed in Ref. 53, by approximating that m ± |n ∓ ≈ 0 for m = n (valid for large couplings), the Hamiltonian in Eq. 24 becomes block diagonal and the eigenenergies and eigenstates can be analytically obtained as follows 53,54