We study a simplified version of the Sachdev-Ye-Kitaev(SYK) model with real interactions by exact diagonalization. Instead of satisfying a continuous Gaussian distribution, the interaction strengths are assumed to be ...We study a simplified version of the Sachdev-Ye-Kitaev(SYK) model with real interactions by exact diagonalization. Instead of satisfying a continuous Gaussian distribution, the interaction strengths are assumed to be chosen from discrete values with a finite separation. A quantum phase transition from a chaotic state to an integrable state is observed by increasing the discrete separation. Below the critical value, the discrete model can well reproduce various physical quantities of the original SYK model,including the volume law of the ground-state entanglement, level distribution, thermodynamic entropy,and out-of-time-order correlation(OTOC) functions. For systems of size up to N=20, we find that the transition point increases with system size, indicating that a relatively weak randomness of interaction can stabilize the chaotic phase. Our findings significantly relax the stringent conditions for the realization of SYK model, and can reduce the complexity of various experimental proposals down to realistic ranges.展开更多
基金This work was supported by the National Natural Science Foundation of China(11434011,11522436,11774425,11704029)the National Key R&D Program of China(2018YFA0306501)+1 种基金the Beijing Natural Science Foundation(Z180013)the Research Funds of Renmin University of China(16XNLQ03 and 18XNLQ15)。
文摘We study a simplified version of the Sachdev-Ye-Kitaev(SYK) model with real interactions by exact diagonalization. Instead of satisfying a continuous Gaussian distribution, the interaction strengths are assumed to be chosen from discrete values with a finite separation. A quantum phase transition from a chaotic state to an integrable state is observed by increasing the discrete separation. Below the critical value, the discrete model can well reproduce various physical quantities of the original SYK model,including the volume law of the ground-state entanglement, level distribution, thermodynamic entropy,and out-of-time-order correlation(OTOC) functions. For systems of size up to N=20, we find that the transition point increases with system size, indicating that a relatively weak randomness of interaction can stabilize the chaotic phase. Our findings significantly relax the stringent conditions for the realization of SYK model, and can reduce the complexity of various experimental proposals down to realistic ranges.
