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arXiv · 1703.02051

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

Shao-Kai Jian·Hong Yao
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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 $ν$=0, violating the Harris criterion. Our higher-dimensional SYK model may provide a promising arena to explore exotic MBL transitions.

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Shao-Kai Jian, Hong Yao. 2017-11-16. Solvable Sachdev-Ye-Kitaev models in higher dimensions: from diffusion to many-body localization. https://doi.org/10.1103/physrevlett.119.206602

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