论文标题
简单排除过程的动力学中的拓扑阶段
Topological phases in the dynamics of the simple exclusion process
论文作者
论文摘要
我们通过数值矩阵产物状态研究了经典随机对称简单排除过程（SSEP）的动力大偏差。我们表明，对于半填充的长时间轨迹，在晶格的偶数和奇数键之间存在足够大的失衡，属于不同的对称性保护拓扑（SPT）阶段。使用张量网络技术，我们从计数场与动力学活性和总跳跃不平衡的情况下获得了较大的偏差（LD）相图。我们显示了高活性琐碎和非平凡的SPT阶段（根据弦序参数分类）的存在，这些阶段被关键阶段或临界点分开。使用倾斜发电机的领先特征状态，从Infinite-System密度矩阵肾上腺素化基团（DMRG）模拟获得，我们构建了一种用于采样LDS的近乎最佳动力学，并表明SPT相显示在稀有随机轨迹的水平上。我们还展示了如何将这些结果扩展到其他填充分数，并讨论对不对称SEP的概括。
We study the dynamical large deviations of the classical stochastic symmetric simple exclusion process (SSEP) by means of numerical matrix product states. We show that for half-filling, long-time trajectories with a large enough imbalance between the number hops in even and odd bonds of the lattice belong to distinct symmetry protected topological (SPT) phases. Using tensor network techniques, we obtain the large deviation (LD) phase diagram in terms of counting fields conjugate to the dynamical activity and the total hop imbalance. We show the existence of high activity trivial and non-trivial SPT phases (classified according to string-order parameters) separated by either a critical phase or a critical point. Using the leading eigenstate of the tilted generator, obtained from infinite-system density matrix renormalisation group (DMRG) simulations, we construct a near-optimal dynamics for sampling the LDs, and show that the SPT phases manifest at the level of rare stochastic trajectories. We also show how to extend these results to other filling fractions, and discuss generalizations to asymmetric SEPs.
