We present random quantum circuit models for nonunitary quantum dynamics of free fermions in one spatial dimension. Numerical simulations reveal that the dynamics tends toward steady states with logarithmic violations of the entanglement area law and power law correlation functions. Moreover, starting with a short-range entangled many-body state, the dynamical evolution of entanglement and correlations quantitatively agrees with the predictions of two-dimensional conformal field theory with a spacelike time direction. We argue that this behavior is generic in nonunitary free quantum dynamics with time-dependent randomness, and we show that the emergent conformal dynamics of two-point functions arises out of a simple “nonlinear master equation.”

中文翻译：

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游离费米子非单位随机动力学中的新兴共形对称性

我们为一个空间维度中的自由费米子的非单位量子动力学提供了随机量子电路模型。数值模拟表明，动力学趋于稳态，纠缠面积定律和幂定律相关函数违反对数关系。此外，从短距离纠缠多体态开始，纠缠和相关​​性的动力学演化在定量上与二维共形场理论在空间时间方向上的预测一致。我们认为，这种行为在具有时间依赖性随机性的非free自由量子动力学中是通用的，并且我们证明了两点函数的新兴共形动力学源于一个简单的“非线性主方程”。