Besides significant electronic correlations, high-temperature superconductors
also show a strong coupling of electrons to a number of lattice modes. Combined
with the experimental detection of electronic inhomogeneities and ordering
phenomena in many high-T_c compounds, these features raise the question as to
what extent phonons are involved in the associated instabilities. Here we
address this problem based on the Hubbard model including a coupling to phonons
in order to capture several salient features of the phase diagram of hole-doped
cuprates. Charge degrees of freedom, which are suppressed by the large Hubbard
U near half-filling, are found to become active at a fairly low doping level.
We find that possible charge order is mainly driven by Fermi surface nesting,
with competition between a near-(pi,pi) order at low doping and antinodal
nesting at higher doping, very similar to the momentum structure of magnetic
fluctuations. The resulting nesting vectors are generally consistent with
photoemission and tunneling observations, evidence for charge density wave
(CDW) order in YBa_2Cu_3O_{7-delta} including Kohn anomalies, and suggestions
of competition between one- and two-q-vector nesting.Comment: This is a revised version of arXiv:1207.5715. 25 pages, 5 figures,
plus Supplement [7 pages, 7 figures], available as a pdf [click on other,
then Download Source, & extract pdf file from zip] Manuscript is under
consideration at the NJ