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

## TL;DR

This paper introduces a higher-dimensional generalization of the SYK model that exhibits a transition from a diffusive metal to a many-body localized phase, providing insights into MBL transitions and their critical properties.

## Contribution

It proposes a new higher-dimensional SYK model demonstrating a direct transition from diffusion to MBL, with numerical evidence and analysis of critical behavior.

## Key findings

- Diffusive phase with maximal chaos for r<r_c
- Vanishing diffusion constant at transition point
- Level statistics change from Wigner-Dyson to Poisson

## 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 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. Remarkably, its diffusive constant $D$ vanishes [$D$$\propto$$ (r_c-r)^{1/2}$] as $r$$\rightarrow$$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.