Dynamics of fluctuations in quantum simple exclusion processes
Dynamics of fluctuations in quantum simple exclusion processes
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DOI：
10.21468/scipostphys.12.1.042
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发表时间：
2021-07
期刊：
影响因子：
5.5
通讯作者：
D. Bernard;F. Essler;Ludwig Hruza;M. Medenjak
中科院分区：
文献类型：
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作者：
D. Bernard;F. Essler;Ludwig Hruza;M. Medenjak
研究了具有周期边界条件的量子非对称简单排斥过程（Q-ASEP）中涨落的动力学性质。Q-ASEP描述了一个由马尔可夫环境引起的具有随机跳跃的无自旋费米子链。我们证明了费米子自由度的涨落服从Lindblad型演化方程，并导出了相应的Lindbladian。我们通过将它们映射到非埃尔米特自旋链来确定基本的代数结构，并证明算子空间碎片成指数级的许多（在系统大小上）扇区，这些扇区在时间演化下是不变的。在二次波动的水平上，我们认为Lindbladian的部门，确定晚时间的量子对称简单排斥过程（Q-SSEP）的特定情况下的动态。我们表明，在某些情况下，相应的块对应于已知的杨巴克斯特可积模型和调查的水平间距统计在其他。我们进行了详细的分析的稳定状态和慢模式，管理后期的时间行为，并表明，动态的波动的观测耦合的线性微分差分方程的封闭集合。这些方程的解决方案的行为基本上是扩散的，但与相关的偏差，在足够晚的时间和大的距离可以描述在一个连续的缩放限制，我们构建。我们数值检查的有效性，在一个显着的时间和空间尺度的缩放限制。这些结果，然后应用到大尺度上的运营商扩展的研究，专注于出的时间有序传播和运营商纠缠。
We consider the dynamics of fluctuations in the quantum asymmetric simple exclusion process (Q-ASEP) with periodic boundary conditions. The Q-ASEP describes a chain of spinless fermions with random hoppings that are induced by a Markovian environment. We show that fluctuations of the fermionic degrees of freedom obey evolution equations of Lindblad type, and derive the corresponding Lindbladians. We identify the underlying algebraic structure by mapping them to non-Hermitian spin chains and demonstrate that the operator space fragments into exponentially many (in system size) sectors that are invariant under time evolution. At the level of quadratic fluctuations we consider the Lindbladian on the sectors that determine the late time dynamics for the particular case of the quantum symmetric simple exclusion process (Q-SSEP). We show that the corresponding blocks in some cases correspond to known Yang-Baxter integrable models and investigate the level-spacing statistics in others. We carry out a detailed analysis of the steady states and slow modes that govern the late time behaviour and show that the dynamics of fluctuations of observables is described in terms of closed sets of coupled linear differential-difference equations. The behaviour of the solutions to these equations is essentially diffusive but with relevant deviations, that at sufficiently late times and large distances can be described in terms of a continuum scaling limit which we construct. We numerically check the validity of this scaling limit over a significant range of time and space scales. These results are then applied to the study of operator spreading at large scales, focusing on out-of-time ordered correlators and operator entanglement.