  The symmetry of the Bloch functions in the conduction band of tetragonal and
orthorhombic La_2CuO_4 is examined for the existence of symmetry-adapted and
optimally localizable (usual or spin-dependent) Wannier functions. It turns out
that such Wannier functions do not exist in the tetragonal phase. In the
orthorhombic phase, on the other hand, the Bloch functions can be unitarily
transformed in three different ways into optimally localizable Wannier
functions: they can be chosen to be adapted to each of the three phases
observed in the pure or doped material, that is, to the antiferromagnetic
phase, to the superconducting phase or to the phase evincing neither magnetism
nor superconductivity. This group-theoretical result is proposed to be
interpreted within a nonadiabatic extension of the Heisenberg model. Within
this model, atomiclike states represented by these Wannier functions are
responsible for the stability of each of the three phases. However, all the
three atomiclike states cannot exist in the tetragonal phase, but are
stabilized by the orthorhombic distortion of the crystal. A simple model is
proposed which might explain the physical properties of the doped material as a
function of the Sr concentration.
