Abstract
Many body localization (MBL) has emerged as a powerful paradigm for understanding non-equilibrium quantum dynamics. Folklore based on perturbative arguments holds that MBL only arises in systems with short range interactions. Here we advance non-perturbative arguments indicating that MBL can arise in systems with long range (Coulomb) interactions. In particular, we show using bosonization that MBL can arise in one dimensional systems with ~ r interactions, a problem that exhibits charge confinement. We also argue that (through the Anderson-Higgs mechanism) MBL can arise in two dimensional systems with log r interactions, and speculate that our arguments may even extend to three dimensional systems with 1/r interactions. Our 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.
Highlights
The phenomenon of many-body localization (MBL) has drawn enormous interest from both the theory [1,2,3,4,5,6,7,8] and experimental [9,10,11,12] communities
We argue that Many-body localization (MBL) can arise in two-dimensional systems with log r interactions, and speculate that our arguments may even extend to three-dimensional systems with 1=r interactions
We demonstrate the viability of this idea, using nonperturbative techniques to treat the interaction, for Coulomb interacting systems in any dimension (i.e., one-dimensional systems with ∼r interactions, two-dimensional systems with log r interactions, 2160-3308=17=7(4)=041021(12)
Summary
The phenomenon of many-body localization (MBL) has drawn enormous interest from both the theory [1,2,3,4,5,6,7,8] and experimental [9,10,11,12] communities. A refinement of this argument [52,53] establishes that two-body interactions with α < 2d break the perturbative expansion Based on these results, a folk theorem has arisen that holds that MBL cannot arise in systems with interactions longer ranged than 1=r2d. A folk theorem has arisen that holds that MBL cannot arise in systems with interactions longer ranged than 1=r2d This excludes a great many experimentally relevant systems, including systems of charges (interacting with a Coulomb interaction in any dimension), and systems with dipolar (1=r3) interactions in two and three dimensions. Our work opens the door to the study of MBL physics in a host of experimentally relevant low-temperature systems with long-range interactions. It differs from Refs. [56,57] in that we do not restrict ourselves to Anderson localization of single spin flips, and consider instead many-body localization
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