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arXiv:2607.09396

Quantum phases in endofullerene zigzag chains

Tobias Serwatka, Muhammad Shaeer Moeed, Roger G. Melko, Pierre–Nicholas Roy

Published Jul 10, 2026• 0 citations
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Abstract

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 $γ$. For LiF, ferroelectric order persists across the full range $60^\circ < γ180^\circ$, with the critical effective dipole moment increasing as the chain bends and parallel alignment becomes less favorable. Near the equilateral configuration ($γ= 60^\circ$), geometric frustration drives a transition to an antiferroelectric Néel-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 $γ= 60^\circ$. 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.

DOI
10.48550/arxiv.2607.09396

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In this dissertation, we study the many-body effects of dipoles in a quasi-one-dimensional zigzag optical lattice, which we call the zigzag chain. We study this system using the Density Matrix Renormalization Group (DMRG) method, which has established itself as the most powerful numerical method to simulate one-dimensional lattices. For the implementation of DMRG, we have used the open-source package Intelligent Tensor, or simply ITensor. The first part of this research focuses on dipoles polarized in the plane of the zigzag chain by an external electric field with the condition that the dipoles can hop around and interact with their first and second neighbors and the number of dipoles is exactly a half of the number of lattice sites. With the interactions much stronger than the hopping, the system comprises of frustrated and non-frustrated regimes owing to the combination of attractive and repulsive interactions in different directions. The consequence is a complex phase diagram featuring the trivial ferromagnetic and antiferromagnetic phases as well as the non-trivial dimerized and superfluid phases. The second part of the research deals with randomly oriented dipoles in the zigzag chain such that each lattice site has exactly one dipole and each dipole interacts with its first and second neighbors but in the absence of any hopping. We study the second system classically allowing many different orientations for each dipole in a lattice site as well as quantum mechanically by allowing a few quantized degrees of freedom to each dipole. The result is a phase diagram showing ferromagnetic, antiferromagnetic and paramagnetic phases.
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