  One of the most puzzling facts about cuprate high-temperature superconductors
in the lightly doped regime is the coexistence of uniform superconductivity
and/or antiferromagnetism with many low-energy charge-ordered states in a
unidirectional charge density wave or a bidirectional checkerboard structure.
Recent experiments have discovered that these charge density waves exhibit
different symmetries in their intra-unit-cell form factors for different
cuprate families. Using a renormalized mean-field theory for a well-known,
strongly correlated model of cuprates, we obtain a number of charge-ordered
states with nearly degenerate energies without invoking special features of the
Fermi surface. All of these self-consistent solutions have a pair density wave
intertwined with a charge density wave and sometimes a spin density wave. Most
of these states vanish in the underdoped regime, except for one with a large
d-form factor that vanishes at approximately 19% doping of the holes, as
reported by experiments. Furthermore, these states could be modified to have a
global superconducting order, with a nodal-like density of states at low
energy.
