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We show that finite systems with conical intersections can exhibitspontaneous symmetry breaking which manifests itself in spatial localization ofeigenstates. This localization has a geometric phase origin and is robustagainst variation of model parameters. The transition between localized anddelocalized eigenstate regimes resembles a continuous phase transition. Thelocalization slows down the low-energy quantum nuclear dynamics at zero and lowtemperatures.

Geometric phase effects in dynamics near conical intersections: Symmetry breaking and spatial localization