Solvable Sachdev-Ye-Kitaev Models in Higher Dimensions: From Diffusion to Many-Body Localization

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 andM free Majorana fermions on each site of the B sublattice, where N andM are large and finite. For r = M/N < r(c) = 1, it describes a diffusive metal exhibiting maximal chaos. Remarkably, its diffusive constant D vanishes [D alpha (r(c) - r)(1/2)] as r -> r(c), implying a dynamical transition to a MBL phase. It is further supported by numerical calculations of level statistics which changes from Wigner-Dyson (r < r(c)) to Poisson (r > r(c)) distributions. Note that no subdiffusive phase intervenes between diffusive and MBL phases. Moreover, the critical exponent nu = 0, violating the Harris criterion. Our higher-dimensional SYK model may provide a promising arena to explore exotic MBL transitions.