论文标题
Yukawa-Syk模型中的量子混乱和相变
Quantum chaos and phase transition in the Yukawa-SYK model
论文作者
论文摘要
我们分析了Yukawa-syk模型的量子混沌行为是填充和温度的函数，该函数描述了$ n $复杂的费米子与零空间维度的$ n $复杂费米和$ m $玻色子之间的随机相互作用，对于有限温度和化学电位上的非弗弗尔米液体和绝缘状态。我们为玻色子和费米子求解了阶梯外相关器（OTOC）的梯子方程。尽管在哈密顿量中出现了化学势，该化学势会明确引入额外的能量量表，但事实证明非弗米液态液态中的费米子和玻色子的OTOC被视为不受影响，而诊断混乱的Lyapunov指数仍然保持最大。随着化学势的增加，已知该系统会经历从临界阶段到间隙绝缘阶段的一阶过渡。我们假设参数空间中区域的边界（元）稳定与Lyapunov指数最大的曲线相吻合。通过在绝缘阶段计算指数，并与稳定边界的数值结果进行比较，我们表明这是合理的。
We analyze the quantum chaotic behavior of the Yukawa-SYK model as a function of filling and temperature, which describes random Yukawa interactions between $N$ complex fermions and $M$ bosons in zero spatial dimensions, for both the non-Fermi liquid and insulating states at finite temperature and chemical potential. We solve the ladder equations for the out-of-time-order correlator (OTOC) for both the bosons and fermions. Despite the appearance of the chemical potential in the Hamiltonian, which explicitly introduces an additional energy scale, the OTOCs for the fermions and bosons in the non-Fermi liquid state turn out to be unaffected, and the Lyapunov exponents that diagnose chaos remain maximal. As the chemical potential increases, the system is known to experience a first-order transition from a critical phase to a gapped insulating phase. We postulate that the boundary of the region in parameter space where each phase is (meta)stable coincides with the curve on which the Lyapunov exponent is maximal. By calculating the exponent in the insulating phase and comparing to numerical results on the boundaries of stability, we show that this is plausible.
