Many-body-localization transition in the one-dimensional SYK model at finite N

We study the generalized Sachdev-Ye-Kitaev (SYK) chain consisting of N (complex or Majorana) fermions per site with random interactions and hoppings between neighboring sites. In the limit of vanishing SYK interactions, from both supersymmetric field theory analysis and numerical calculations we find that the random-hopping model exhibits Anderson localization at finite N, irrespective of the parity of N. Moreover, the localization length scales linearly with N, implying the absence of Anderson localization only at N=∞. For finite SYK interactions, by performing the exact diagonalization we show that there is a dynamic phase transition from many-body localization to thermal diffusion as interaction strength exceeds a critical value Jc. In addition, we find that the critical interaction strength Jc decreases with the increase of N, consistent with the analytical result of Jc/t ∝ 1/(N^5/2logN), derived from the weakly interacting limit.
[1] Xin Dai, Shao-Kai Jian, Hong Yao, arXiv:1802.10029