Strong-coupling expansions for the anharmonic Holstein model and for the   Holstein-Hubbard model
  A strong-coupling expansion is applied to the anharmonic Holstein model and to the Holstein-Hubbard model through fourth order in the hopping matrix element. Mean-field theory is then employed to determine transition temperatures of the effective (pseudospin) Hamiltonian. We find that anharmonic effects are not easily mimicked by an on-site Coulomb repulsion, and that anharmonicity strongly favors superconductivity relative to charge-density-wave order. Surprisingly, the phase diagram is strongly modified by relatively small values of the anharmonicity. 
J. K. Freericks (Georgetown University) and G. D. Mahan (University of   Tennessee and Oak Ridge National Laboratory)