Stability of quasiperiodic chains to quantum avalanches*

In one dimension, it is conjectured that full many-body localization is unstable if the localization length exceeds a threshold value. The instability is due to the presence of rare ergodic Griffiths regions; each such region thermalizes its environment and grows, resulting in a (slow) avalanching process of thermalization. We show that weakly interacting chains with quasiperiodic potentials violate this conjecture because the sparse local structure of the l-bits prevents thermalization near an ergodic region. Our work identifies the first qualitative difference between random and quasi-periodic localization and suggests new experimental tests of avalanche instabilities.