Time-Dependent Variational Approach to Ground-State Phase Transition and Phonon Dispersion Relation of the Quantum Double-Well Model

The ground-state phase transition and the phonon dispersion relation of the quantum double-well model are studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction. The single-particle state is taken to be a frozen Jackiw--Kerman wavefunction. Under the condition of minimum uncertainty relation, we obtain an effective classical Hamiltonian for the system and equations of motion for the particle's expectation values. It is shown that the effective substrate potential transits from a symmetric double-well potential to a symmetric single-well potential, and the ground state exhibits a transition from a broken symmetry phase to a restored symmetry phase as increasing the strength of quantum fluctuations. We also obtain the phonon dispersion relations and the phonon gaps at the two phases.