  Understanding similarities and differences between the cuprate and nickelate
superconductors is drawing intense current interest. Competing charge orders
have been observed recently in the $undoped$ infinite-layer nickelates in sharp
contrast to the $undoped$ cuprates which exhibit robust antiferromagnetic
insulating ground states. The microscopic mechanisms driving these differences
remain unclear. Here, using in-depth first-principles and many-body theory
based modeling, we show that the parent compound of the nickelate family,
LaNiO$_2$, hosts a charge density wave (CDW) ground state with the predicted
wavevectors in accord with the corresponding experimental findings. The CDW
ground state is shown to be connected to a multi-orbital Peierls distortion.
Our study points to the key role of electron-phonon coupling effects in the
infinite-layer nickelates.
