Ground-state phase diagram of the 1-D Holstein–Hubbard model

Highlights: • 1-D Holstein–Hubbard model is studied using six unitary transformations. • Electron-density-dependent phonon correlation is introduced for the first time. • Phonon-averaged effective Hamiltonian is solved exactly by the Bethe ansatz method. • Present GS energy is found lower than those obtained by previous variational methods. • A wider metallic phase is obtained at the CDW–SDW cross-over region. -- Abstract: The Holstein–Hubbard model is investigated in one-dimension at half filling employing a series of unitary transformations taking into account the coherence and correlation of phonons. To treat the phonon subsystem more accurately a new squeezing transformation is introduced to incorporate the electron-density-dependent onsite phonon correlations to lower the energy further. The effective electronic Hamiltonian is next obtained by averaging the transformed Hamiltonian with respect to the zero-phonon state and the resulting effective electronic Hamiltonian is solved exactly using the method of Bethe ansatz. Finally the ground state is obtained by minimizing the energy with respect to all the variational parameters. The present method gives better results for the ground state energy of the system and also suggests the existence of a wider intermediate metallic phase at the charge-density-wave–spin-density-wave crossover region, which was first predicted by Takada and Chatterjee and later supported by Krishna and Chatterjee.