Many body localization with long range interactions*

Many-body localization (MBL) has emerged as a powerful paradigm for understanding nonequilibrium quantum dynamics. Folklore based on perturbative arguments holds that MBL arises only in systems with short-range interactions. I will present nonperturbative arguments indicating that MBL can arise in systems with long-range (Coulomb) interactions, through a mechanism dubbed “order enabled localization.” In particular, one can show using bosonization that MBL can arise in one-dimensional systems with ∼r interactions, a problem that exhibits charge confinement. One can also show that (through the Anderson-Higgs mechanism) MBL can arise in two-dimensional systems with log(r) interactions, and perhaps even in three-dimensional systems with 1/r interactions. The extension to three dimensions requires developing a theory of localization of extended quantum objects. The arguments are asymptotic (i.e., valid up to rare region corrections), yet they open the door to investigation of MBL physics in a wide array of long-range interacting systems where such physics was previously believed not to arise. They also open the door to using MBL to stabilize driven superconductivity.

Rahul M. Nandkishore and S. L. Sondhi, Phys. Rev. X 7 041021 (2017)
Michael Pretko and Rahul M. Nandkishore, Phys. Rev. B 98, 134301 (2018)