Gross-Pitaevskii equations for the molecular achiral-chiral transitions*

In the mean-field theory, the stabilization of chiral molecules is understood as a quantum phase transition where the mean-field ground state of molecules changes from the achiral eigenstate of the molecular Hamiltonian to one of the degenerated chiral states due to the increase of the intermolecular interaction. However, the existing mean-field models are either unavailable to chiral molecules whose electric dipoles do not change in sign for |L〉 and |R〉 or with free parameters. In this work, starting from the Many-body Hamiltonian with electric dipole-dipole interaction, we give the static Gross-Pitaevskii equations in the vibrational dimension. Our model can be applied to all chiral molecules and has no free parameters.