  We investigate the impact of quantum vibronic coupling on the electronic
properties of solid-state spin defects using stochastic methods and first
principles molecular dynamics with a quantum thermostat. Focusing on the
negatively charged nitrogen-vacancy center in diamond as an exemplary case, we
found a significant dynamic Jahn-Teller splitting of the doubly degenerate
single-particle levels within the diamond's band gap, even at 0 K, with a
magnitude exceeding 180 meV. This pronounced splitting leads to substantial
renormalizations of these levels and subsequently, of the vertical excitation
energies of the doubly degenerate singlet and triplet excited states. Our
findings underscore the pressing need to incorporate quantum vibronic effects
in first-principles calculations, particularly when comparing computed vertical
excitation energies with experimental data. Our study also reveals the
efficiency of stochastic thermal line sampling for studying phonon
renormalizations of solid-state spin defects.
