论文标题
拓扑订购的多体局部系统的本地运动积分
Local Integrals of Motion for Topologically Ordered Many-Body Localized Systems
论文作者
论文摘要
通常使用其局部运动积分来描述多体局部（MBL）系统，对于自旋系统而言，通常认为这是一组现场自旋Z运算符的局部单一变换。我们表明，对于拓扑订购的MBL系统，此假设无法持有。使用合适的定义在任何空间维度中捕获此类系统，我们演示了许多特征，包括目前的MBL拓扑顺序：（i）对于所有特征态都相同； （ii）特征与保留MBL的任何扰动； （iii）意味着，在拓扑非平凡的歧管上，一组完整的运动积分必须以局部不合理的不缩放的威尔逊环路的形式包括非局部性。我们的方法非常适合张量 - 网络方法，并且有望使这些方法解决高度兴奋的有限大小拓扑特征，尽管它们的能量重叠。我们说明了关于无序的基塔夫链，复曲面代码和X-Cube模型的方法。
Many-body localized (MBL) systems are often described using their local integrals of motion, which, for spin systems, are commonly assumed to be a local unitary transform of the set of on-site spin-z operators. We show that this assumption cannot hold for topologically ordered MBL systems. Using a suitable definition to capture such systems in any spatial dimension, we demonstrate a number of features, including that MBL topological order, if present: (i) is the same for all eigenstates; (ii) is robust in character against any perturbation preserving MBL; (iii) implies that on topologically nontrivial manifolds a complete set of integrals of motion must include nonlocal ones in the form of local-unitary-dressed noncontractible Wilson loops. Our approach is well suited for tensor-network methods, and is expected to allow these to resolve highly-excited finite-size-split topological eigenspaces despite their overlap in energy. We illustrate our approach on the disordered Kitaev chain, toric code, and X-cube model.
