Abstract
We investigate the effect of coupling Anderson localized particles in one dimension to a system of marginally localized phonons having a symmetry protected delocalized mode at zero frequency. This situation is naturally realized for electrons coupled to phonons in a disordered nanowire as well as for ultracold fermions coupled to phonons of a superfluid in a one-dimensional disordered trap. To determine if the coupled system can be many-body localized we analyze the phonon-mediated hopping transport for both the weak and strong coupling regimes. We show that the usual variable-range hopping mechanism involving a low-order phonon process is ineffective at low temperature due to discreteness of the bath at the required energy. Instead, the system thermalizes through a many-body process involving exchange of a diverging number n∝-logT of phonons in the low temperature limit. This effect leads to a highly singular prefactor to Mott's well-known formula and strongly suppresses the variable range hopping rate. Finally, we comment on possible implications of this physics in higher dimensional electron-phonon coupled systems.
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