Variable-range hopping through marginally localized phonons

Recently there is a surge of activities in interacting quantum systems subjected to strong disorder. These systems pose fundamental questions about quantum dynamics in closed systems, which might fail to thermalize due to the phenomenon of many-body localization (MBL). After a general introduction to MBL, I will discuss the possibility to realize a MBL state of particles coupled to gapless and asymptotically delocalized phonons. This is in contrast to the general belief that such coupling to phonons would inevitably lead to delocalization through phonon assisted hopping and the well-known variable range hopping (VRH) transport. Specifically, we consider a system of electrons coupled to a one dimensional random harmonic chain and analyze the phonon-mediated hopping transport for both weak and strong coupling regimes [1]. We show that the usual VRH transport via low-order phonon processes is absent in this system and at low temperature the system could only thermalize through arbitrary high-order process leading to a modified VRH rate. If time permits, I will briefly mention our ongoing work on thermalization of electrons coupled to random Heisenberg chain and some preliminary dynamical mean-field theory (DMFT) results on MBL in disordered Hubbard model.

[1] S. Banerjee and E. Altman, arXiv:1511.03676 (2015).