# Vibronic Ground-state Degeneracies and the Berry Phase: A Continuous Symmetry Perspective

## TL;DR

This paper presents a geometric approach to prove that the electronic ground-state Berry phase is unavoidable in certain Jahn-Teller models with high symmetry, explaining the fundamental origin of vibronic degeneracy.

## Contribution

It introduces a continuous symmetry perspective to establish the inevitability of the Berry phase in Jahn-Teller models with maximal symmetry and multiple intersecting electronic states.

## Key findings

- Proves the electronic Berry phase is unavoidable in specific Jahn-Teller models.
- Links vibronic ground-state degeneracy directly to the Berry phase.
- Provides a geometric construction applicable to models with N > 2 states.

## Abstract

We develop a geometric construction to prove the inevitability of the electronic ground-state (adiabatic) Berry phase for a class of Jahn-Teller models with maximal continuous symmetries and N > 2 intersecting electronic states. Given that vibronic ground-state degeneracy in JT models may be seen as a consequence of the electronic Berry phase, and that any JT problem may be obtained from the subset we investigate in this letter by symmetry-breaking, our arguments reveal the fundamental origin of the vibronic ground-state degeneracy of JT models.