Entanglement mean field theory and MBL in two dimensions

We present “entanglement mean field theory”, a statistical theory of the subsystem entanglement in eigenstates. This theory applies across the MBL-thermal phase transition to a class of models with “central seed” geometry. The predictions of the theory show good agreement with numerics, even for subsystems which are intermediate to localised and thermal.

 

We apply this model to analyse the possibility of MBL in two dimensions with quasi-periodic modulation and show there exists a class of quasi-periodic two-dimensional models with a stable MBL phase. In contrast, for random modulation the presence of thermal bubbles always leads to avalanches in the thermodynamic limit.