It is typically assumed that disorder is essential to realize Anderson localization. Recently, a number of proposals have suggested that an interacting, translation invariant system can also exhibit localization. We examine these claims in the contex
t of a one-dimensional spin ladder. At intermediate time scales, we find slow growth of entanglement entropy consistent with the phenomenology of many-body localization. However, at longer times, all finite wavelength spin polarizations decay in a finite time, independent of system size. We identify a single length scale which parametrically controls both the eventual spin transport times and the divergence of the susceptibility to spin glass ordering. We dub this long pre-thermal dynamical behavior, intermediate between full localization and diffusion, quasi-many body localization.
We demonstrate how to build a simulation of two dimensional physical theories describing topologically ordered systems whose excitations are in one to one correspondence with irreducible representations of a Hopf algebra, D(G), the quantum double of
a finite group G. Our simulation uses a digital sequence of operations on a spin lattice to prepare a ground vacuum state and to create, braid and fuse anyonic excitations. The simulation works with or without the presence of a background Hamiltonian though only in the latter case is the system topologically protected. We describe a physical realization of a simulation of the simplest non-Abelian model, D(S_3), using trapped neutral atoms in a two dimensional optical lattice and provide a sequence of steps to perform universal quantum computation with anyons. The use of ancillary spin degrees of freedom figures prominently in our construction and provides a novel technique to prepare and probe these systems.
