非酉随机动力学中的多重分形
Multifractality in non-unitary random dynamics
摘要：
研究了一维非幺正随机量子动力学稳态波函数的多重分形性。我们主要研究两类随机系统：混合Clifford电路模型和非幺正自由费米子动力学。在混合Clifford模型中，我们利用稳定子态的性质，将测量驱动跃迁映射到有效图空间中的安德森局域化跃迁。我们证明了具有非零测量率的体积律相位在图空间中是非遍历的，并表现出弱的多重分形行为。我们将同样的方法应用到混合Clifford量子自动机电路中，得到了体积律阶段类似的多重分形。对于具有临界定态的非幺正随机自由费米子系统，我们计算了单粒子波函数概率分布的矩，证明了它也是弱多重分形的，并且在实空间中有很强的变化.
英文摘要：
We explore the multifractality of the steady state wave function in non-unitary random quantum dynamics in one dimension. We focus on two classes of random systems: the hybrid Clifford circuit model and the non-unitary free fermion dynamics. In the hybrid Clifford model, we map the measurement driven transition to an Anderson localization transition in an effective graph space by using properties of the stabilizer state. We show that the volume law phase with nonzero measurement rate is non-ergodic in the graph space and exhibits weak multifractal behavior. We apply the same method to the hybrid Clifford quantum automaton circuit and obtain similar multifractality in the volume law phase. For the non-unitary random free fermion system with a critical steady state, we compute the moments of the probability distribution of the single particle wave function and demonstrate that it is also weakly multifractal and has strong variations in real space.
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