  We introduce a theory that exposes the fundamental and previously overlooked
connection between the correlation among electrons and the degree of quantum
coherence of electronic states in matter. For arbitrary states, the effects
only decouple when the electronic dynamics induced by the nuclear bath is
pure-dephasing in nature such that $[H^{S},H^{SB}]=0$, where $H^{S}$ is the
electronic Hamiltonian and $H^{SB}$ is the electron-nuclear coupling. We
quantitatively illustrate this connection via exact simulations of a
Hubbard-Holstein molecule using the Hierarchical Equations of Motion that show
that increasing the degree of electronic interactions can enhance or suppress
the rate of electronic coherence loss.
