Quantum fluctuations and the ground-state phase diagram of the strong-coupling Holstein-Hubbard model

A Grassmann functional integration technique is applied to the anisotropic pseudospin Hamiltonian derived from the Holstein-Hubbard model with strong electron-phonon coupling. It is found that in those regions of the low-temperature phase diagram where superconductivity and the charge-density wave coexist already the static and homogeneous saddle point solution of the resulting field theory yields a ground-state energy which is lower than the classical result corresponding to the usual mean-field solution. This is due to the presence of quantum fluctuations and leads to new ground-state phase boundaries quantitatively different from those obtained in previous work by conventional operator decoupling schemes.