4. Multiscale QED solvers
This is the multisclae QED moduel for polariton chemistry: (TBA)
This is a collection of solvers, including mean-field and many-body methods, for solving the QED Hamiltonian
\[\begin{split}\hat{H} = & \hat{H}_M + \sum_\alpha \omega_\alpha b^\dagger b + \sum_\alpha \sqrt{\frac{\omega_\alpha}{2}}\boldsymbol{D}\cdot \boldsymbol{\lambda}_\alpha (b^\dagger+b) + \frac{1}{2}\sum_\alpha (\boldsymbol{D}\cdot \boldsymbol{\lambda}_\alpha)^2\\
= & \hat{H}_M + \sum_\alpha \omega_\alpha b^\dagger b + \sum_\alpha \sqrt{\frac{\omega_\alpha}{2}}\lambda_\alpha \boldsymbol{D}\cdot \boldsymbol{e}_\alpha (b^\dagger+b)
+ \frac{1}{2}\sum_\alpha (\lambda_\alpha\boldsymbol{D}\cdot \boldsymbol{e}_\alpha)^2\end{split}\]
where
\(\lambda_\alpha=\sqrt{\frac{1}{\epsilon V_\alpha}}\) and \(e_\alpha\) are the amplitude and unit vector of the photon mode, respectively.
\(V\) is the cavity volume.
\(\omega\) is the energy of the photon mode.
\(\hat{H}_M\) is the molecular Hamiltonian, including electronic (and nuclear if needed) DOFs.
\(\boldsymbol{D}\) is dipole operator.