Ground-state symmetry classification for a non-isolated tunnelling particle

We demonstrate that the ground energy of a two-level system coupled with a bosonic environment can be labelled with a quantum number related to the total excitation number operator and independent of the coupling strength. Our approach is exact and is based on operator methods combining symmetry considerations with general properties of the lowest energy state. The relevance of our result in connection with the nature of the transition from the weak to strong coupling regime is briefly discussed.