Thermal inclusions: how one spin can destroy a many-body localized phase

Many-body localized (MBL) systems lie outside the framework of statistical mechanics, as they fail to equilibrate under their own quantum dynamics. Even basic features of MBL systems such as their stability to thermal inclusions and the nature of the dynamical transition to thermalizing behavior remain poorly understood. We study a simple model to address these questions: a two level system interacting with strength $J$ with $N\gg 1$ localized bits subject to random fields. On increasing $J$, the system transitions from a MBL to a delocalized phase on the \emph{vanishing} scale $J_c(N) \sim 1/N$, up to logarithmic corrections. In the transition region, the single-site eigenstate entanglement entropies exhibit bi-modal distributions, so that localized bits are either "on" (strongly entangled) or "off" (weakly entangled) in eigenstates. The clusters of "on" bits vary significantly between eigenstates of the \emph{same} sample, which provides evidence for a heterogenous discontinuous transition out of the localized phase in single-site observables. We obtain these results by perturbative mapping to bond percolation on the hypercube at small $J$ and by numerical exact diagonalization of the full many-body system. Our results imply the MBL phase is unstable in systems with short-range interactions and quenched randomness in dimensions $d$ that are high but finite.Comment: 17 pages, 12 figure

Determining North Atlantic meridional transport variability from pressure on the western boundary: a model investigation.

In this paper we investigate the possibility of determining North Atlantic meridional transport variability using pressure on the western boundary, focusing on the 42degN latitude of the Halifax WAVE array. We start by reviewing the theoretical foundations of this approach. Next we present results from a model analysis, both statistical and dynamic, that demonstrate the feasibility of the approach. We consider how well we can quantify the meridional transport variability at 42degN given complete knowledge of bottom pressure across the basin, and to what degree this quantification is degraded by first ignoring the effect of intervening topography, and then by using only bottom pressure on the western boundary. We find that for periods of greater than one year we can recover more than 90% of the variability of the main overturning cell at 42degN using only the western boundary pressure, provided we remove the depth-average boundary pressure signal. This signal arises from a basin mode of bottom pressure variability, which has power at all timescales, but that does not in truth have a meridional transport signal associated with it, and from the geostrophic depth-independent compensation of the Ekman transport. An additional benefit of the removal of the depth-average pressure is that this high-frequency Ekman signal, which is essentially noise as far as monitoring the MOC for climatically important changes is concerned, is clearly separated from other modes