Local integrals of motion for topologically ordered many-body localized systems

T. Wahl, B. B'eri
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引用次数: 4

Abstract

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.
拓扑有序多体定域系统运动的局部积分
多体局域化(MBL)系统通常用它们的局部运动积分来描述,对于自旋系统,通常假定它是现场自旋-z算子集合的局部酉变换。我们证明这种假设对于拓扑有序的MBL系统不成立。使用一个合适的定义来捕获任何空间维度的这样的系统,我们证明了许多特征,包括MBL拓扑顺序,如果存在:(i)对于所有特征态都是相同的;(ii)对任何保持MBL的扰动具有鲁棒性;(iii)表明在拓扑非平凡流形上,运动积分的完备集必须包含局部酉穿戴不可收缩威尔逊环形式的非局部积分。我们的方法非常适合于张量网络方法,并且有望允许这些方法解决高度激发的有限尺寸分裂拓扑特征空间,尽管它们在能量上重叠。我们用无序Kitaev链、环向码和x立方模型来说明我们的方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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