Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite $N$

Xin Dai; Shao-Kai Jian; Hong Yao

doi:10.1103/PhysRevB.100.235144

paper

Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite $N$

arXiv:1802.10029 · doi:10.1103/PhysRevB.100.235144

Abstract

Many key features of the higher-dimensional Sachdev-Ye-Kitaev (SYK) model at {\it finite} $N$ remain unknown. Here we study the SYK chain consisting of $N$ ( $N$ $\geq$ $2$ ) 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 no Anderson localization \textit{only} at $N = \infty$ . For finite SYK interaction $J$ , from the exact diagonalization we show that there is a dynamic phase transition between many-body localization and thermal diffusion as $J$ exceeds a critical value $J_{c}$ . In addition, we find that the critical value $J_{c}$ decreases with the increase of $N$ , qualitatively consistent with the analytical result of $J_{c} / t \propto \frac{1}{N ^{5/2} l o g N}$ derived from the weakly interacting limit.

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Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite $N$

Abstract

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Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite N

Abstract

References in corpus (76)

Cited by in corpus (10)

Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite $N$