Orbital ordering in undoped manganites via a generalized Peierls instability

We study the ground state orbital ordering of $LaMnO_3$, at weak electron-phonon coupling, when the spin state is A-type antiferromagnet. We determine the orbital ordering by extending to our Jahn-Teller system a recently developed Peierls instability framework for the Holstein model [1]. By using two-dimensional dynamic response functions corresponding to a mixed Jahn-Teller mode, we establish that the $Q_2$ mode determines the orbital order.