Quantum phases in endofullerene zigzag chains

We employ large-scale density matrix renormalization group calculations to study the quantum phases of dipolar molecules confined in bent (zigzag) endofullerene chains, as a function of the chain angle $\gamma$. For LiF, ferroelectric order persists across the full range $60^\circ < \gamma 180^\circ$, with the critical effective dipole moment increasing as the chain bends and parallel alignment becomes less favorable. Near the equilateral configuration ($\gamma = 60^\circ$), geometric frustration drives a transition to an antiferroelectric N\'eel-ordered phase in which neighboring dipoles anti-align along the chain axis. We show that capturing this reorientation requires including dipolar couplings beyond the nearest-neighbor approximation, since next-nearest-neighbor interactions become equally strong at $\gamma = 60^\circ$. For confined water, o-D$_2$O reproduces both ordered phases, whereas p-H$_2$O -- owing to its large rotational constants -- develops no order at any chain angle despite the enhanced coordination of the bent geometry. Because a zigzag chain is the narrowest stripe of a two-dimensional lattice, these results suggest that engineered endofullerene layers could host a rich variety of dipole-ordered quantum phases beyond the ferroelectric ordering observed in previous work.