Title: Continuous vibronic symmetries in Jahn-Teller models,
Abstract: We develop a systematic study of Jahn-Teller (JT) models with continuous
symmetries by explor- ing their algebraic properties. The compact symmetric
spaces corresponding to JT models carrying a Lie group symmetry are identified,
and their invariants used to reduce their adiabatic potential energy surfaces
into orbit spaces. Each orbit consists of a set of JT distorted molecular
structures with equal adiabatic electronic spectrum. Molecular motion may be
decomposed into pseudorota- tional and radial. The former preserves the orbit,
while the latter maps an orbit into another. The dimensionality and topology of
the internal space of each orbit depends on the number of degener- ate states
in its adiabatic electronic spectra. Furthermore, qualitatively different
pseudorotational modes occur in orbits of different types. We also provide a
simple proof that the electronic spectrum for the space of JT minimum-energy
structures (trough) displays a universality predicted by the epikernel
principle. This result is in turn used to prove the topological equivalence
between bosonic (fermionic) JT troughs and real (quaternionic) projective
spaces, a conclusion which has outstanding physical consequences, as explained
in our work. The relevance of our study for the more common case of JT systems
with only discrete point group symmetry, and for generic asymmetric molecular
systems with conical intersections involving more than two states is likewise
discussed. In particular, we show that JT models with continuous symmetries
present the simplest models of conical intersections among an arbitrary number
of electronic state crossings.