  We report the dielectric, magnetic, and ultrasonic properties of a
one-dimensional organic salt TTF-QBr$_3$I. These indicate that TTF-QBr$_3$I
shows a ferroelectric spin-Peierls (FSP) state in a quantum critical regime. In
the FSP state, coupling of charge, spin, and lattice leads to emergent
excitation of spin solitons as topological defects. Amazingly, the solitons are
highly mobile even at low temperatures, although they are normally stationary
because of pinning. Our results suggest that strong quantum fluctuations
enhanced near a quantum critical point enable soliton motion governed by
athermal relaxation. This indicates the realization of quantum topological
transport at ambient pressure.
