Returning dimensionality to many-body localization.

Anushya Chandran,

Perimeter Institute for Theoretical Physics,
Ontario, Canada

In the presence of sufficient quenched disorder, generic quantum systems can fail to equilibrate under their intrinsic dynamics, even when highly excited. This is the phenomenon of many-body localization (MBL), which can be understood abstractly as localization in Hilbert space or somewhat more physically, as a consequence of a complete set of spatially local conserved bits (l-bits) that block local equilibration. These l-bits explain a number of exotic properties of MBL systems including their perfect  insulating behavior at all energy densities and their ability to exhibit quantum orders in excited states that are forbidden by statistical mechanics. Prima facie, MBL is a single phenomenon in all dimensions much like its non-interacting cousin, Anderson localization.                                                                                

In this talk I will show that this viewpoint is too naive and the MBL depends in important ways on spatial dimensionality. First, I will show that the little understood direct transition between the localized and conventional thermal phases must have associated exponents that are d-dependent by deriving rigorous lower bounds on these exponents. Second, and more strikingly, I will argue that in d>=3, l-bits are not stable and thus that the MBL phase is qualitatively different from that in d=1. I will end with a more general phenomenology of MBL in any dimension in terms of approximately conserved l*-bits and discuss experimental consequences.