论文标题
运营商纠缠下的崛起和跌落，并逐渐上升
Rise and fall, and slow rise again, of operator entanglement under dephasing
论文作者
论文摘要
操作员空间纠缠熵，或简单的“操作员纠缠”（OE），是量子运算符及其近似性的复杂性的指标。我们研究了经历了耗散性进化的1D多体模型的密度矩阵的OE。预计，在最初的线性生长让人联想到单一淬灭动力学之后，随着系统发展到简单的固定状态，OE应被耗散过程抑制。令人惊讶的是，我们发现这种情况破坏了最根本的耗散机制之一：dephasing。在Dephasing下，在最初的“上升和跌落”之后，OE可以再次上升，长时间对数增加。使用MPO模拟的组合，用于无限长度和分析论点有效的链条，我们证明了这种增长是$ u（1）$保护法固有的。我们认为，在XXZ旋转模型和Bose-Hubbard模型中，OE长时间以$ \ frac {1} {1} {1} {4} {4} {4} \ log_2 t $长期生长，而Fermi-Hubbard模型则为$ \ frac {1} {2} {2} \ log_2 t $。我们将这种行为追溯到异常的经典扩散过程。
The operator space entanglement entropy, or simply 'operator entanglement' (OE), is an indicator of the complexity of quantum operators and of their approximability by Matrix Product Operators (MPO). We study the OE of the density matrix of 1D many-body models undergoing dissipative evolution. It is expected that, after an initial linear growth reminiscent of unitary quench dynamics, the OE should be suppressed by dissipative processes as the system evolves to a simple stationary state. Surprisingly, we find that this scenario breaks down for one of the most fundamental dissipative mechanisms: dephasing. Under dephasing, after the initial 'rise and fall' the OE can rise again, increasing logarithmically at long times. Using a combination of MPO simulations for chains of infinite length and analytical arguments valid for strong dephasing, we demonstrate that this growth is inherent to a $U(1)$ conservation law. We argue that in an XXZ spin-model and a Bose-Hubbard model the OE grows universally as $\frac{1}{4} \log_2 t$ at long times, and as $\frac{1}{2} \log_2 t$ for a Fermi-Hubbard model. We trace this behavior back to anomalous classical diffusion processes.
