Abstract
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 of the B sublattice, where N and M 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∝(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 ν=0, violating the Harris criterion. Our higher-dimensional SYK model may provide a promising arena to explore exotic MBL transitions.
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