  We explore a novel coupling mechanism of electrons with the transverse
optical (TO) phonon branch in a regime when the TO mode becomes highly
anharmonic and drives the ferroelectric phase transition. We show that this
anharmonicity, which leads to a collective motion of ions, is able to couple
electronic and lattice displacement fields. An effective correlated
electron-ion dynamics method is required to capture the effect of the onset of
the local electric polarization due to this collective behavior close to the
quantum critical point. We identify an intermediate temperature range where an
emergent phonon drag may contribute substantially to thermoelectric
conductivity in this regime. We find that, under optimal conditions, this extra
contribution may be larger than values achieved so far in the benchmark
material, PbTe. In the last part we make a case for the importance of our
results in the generic problem of anharmonic electron-lattice dynamics.
