Many-body localization beyond eigenstates in all dimensions

Abstract

Isolated quantum systems with quenched randomness exhibit many-body localization (MBL), wherein they do not reach local thermal equilibrium even when highly excited above their ground states. It is widely believed that individual eigenstates capture this breakdown of thermalization at finite size. We show that this belief is false in general and that a MBL system can exhibit the eigenstate properties of a thermalizing system. We propose that localized approximately conserved operators (l * -bits) underlie localization in such systems. In dimensions d > 1, we further argue that the existing MBL phenomenology is unstable to boundary effects and gives way to l * -bits. Physical consequences of l * -bits include the possibility of an eigenstate phase transition within the MBL phase unrelated to the dynamical transition in d = 1 and thermal eigenstates at all parameters in d > 1. Near-term experiments in ultra-cold atomic systems and numerics can probe the dynamics generated by boundary layers and emergence of l * -bits.

The eigenstate thermalization hypothesis in constrained Hilbert spaces: A case study in non-Abelian anyon chains

“…Recent experiments in cold gases have quantitatively tested the effects of the GGE in 1D [75][76][77] . Strongly disordered systems can also generically fail to thermalize in the thermodynamic limit and violate ETH if they are many-body localized 49,67,69,78,79 . Integrability underlies this failure (at least in strongly disordered regimes 80,81 ), although there is no GGE description of the steady state.…”

Dynamically enriched topological orders in driven two-dimensional systems

“…as L ⊥ ∼ L 2 ). In this way, the time scale for the bulk thermalization diverges much faster than the edge-thermalization timescale, so that there is a well-defined infinite system long time limit in which the edge is in a thermal steady state, but the bulk is still localized (see also [49]). …”

Stability and instability towards delocalization in many-body localization systems

“…In our theory, the cross-over region is fully thermal, but the structure (spectral) factors of operators supported in that region become very narrow as their support approaches the MBL system. An intruiging prediction of our theory is that a localized system with interactions that decay slower than exponentially with distance, is not stable with respect to large ergodic grains, though the thermalization time for such a system can still be enormously large, thus making it localized for all practical purposes Counterintuitive as it might be, the idea that a few degrees of freedom can delocalize a much larger number of localized degrees of freedom, has by now been put forward already by several authors [25][26][27] . Numerics for larger systems is however needed to nail down this instability.…”