1205.0026 (Ronen Vosk et al.)

Many-body localization in one dimension as a dynamical renormalization
group fixed point    [PDF]

Ronen Vosk, Ehud Altman

We formulate a dynamical real space renormalization group approach to describe the time evolution of a random spin-1/2 chain, or interacting fermions, initialized in a state with fixed particle positions. Within this approach we identify a many-body localized state of the chain as a dynamical infinite randomness fixed point. Near this fixed point our method becomes asymptotically exact, allowing analytic calculation of time dependent quantities. In particular we recover and explain the origin of the striking universal growth of the entanglement entropy as log(t) seen in recent numerical simulations, as well as the delay of this growth by a time inversely proportional to the interaction strength. We predict that the logarithmic growth will revert to log^2(t) after an emergent long time scale, parametrically well separated from the initial delay time. The particle number fluctuations by contrast exhibit much slower growth as log(log(t)) indicating blocked particle transport. Lack of true thermalization in the long time limit is attributed to an infinite set of approximate integrals of motion revealed in the course of the RG flow, which become asymptotically exact conservation laws at the fixed point. Hence we identify the many-body localized state with an emergent generalized Gibbs ensemble.

View original: http://arxiv.org/abs/1205.0026