  In the present work we discuss the propagation of excitons across a
one-dimensional Su-Schrieffer-Heeger lattice, which possesses both harmonic
oscillations and weak quartic anharmonicities. When quantizing these
vibrational degrees of freedom we identify several phonon-conserving
nonlinearities, each one with a different impact on the excitonic transport.
Our analysis identifies a dominant nonlinear correction to the phonon hopping
which leads to a strong enhancement of exciton conduction compared to a purely
linear vibrational dynamics. Thus quartic lattice nonlinearities can be
exploited to induce transitions from localized to delocalized transport, even
for very weak amplitudes.
