Solvable Sachdev-Ye-Kitaev models in higher dimensions: from diffusion to many-body localization

Understand

Many aspects of many-body localization (MBL) transitions remain elusive so far.

• Here, we propose a higher-dimensional generalization of the Sachdev-Ye-Kitaev (SYK) model and show that it exhibits a MBL transition.
• The model on a bipartite lattice has $N$ Majorana fermions with SYK interactions on each site of the $A$ sublattice and $M$ free Majorana fermions on each site the of $B$ sublattice, where $N$ and $M$ are large and finite.
• For $r$$\equiv$$M/N\!<\!r_c$=1, it describes a diffusive metal exhibiting maximal chaos.