论文标题
拓扑壁板纠缠：一维拓扑超导体的非局部秩序参数
Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors
论文作者
论文摘要
在过去的二十年中，确定表征拓扑系统（尤其是拓扑超导体和拓扑绝缘子）的基于纠缠的顺序参数，特别是拓扑超导体和拓扑绝缘子，对量子物质物理物理学仍然是一个主要挑战。在这里，我们表明，端到端，长距离的，两分的壁板在一个多体系统的边缘之间被定义的多体系统的边缘之间，是根据边缘到边缘到边缘的量子有条件的相互信息定义的，是一维拓扑超导体的自然非内置非内部阶订单参数，以及在Quasi的一维差异中。对于整个拓扑阶段的Kitaev链，将边缘式纠缠量化为原木（2）/2，最大铃铛纠缠的一半，在微不足道的阶段消失。这种拓扑壁板的纠缠在量子相变的情况下表现出正确的缩放，在存在相互作用的情况下是稳定的，并且对疾病和局部扰动非常有力。边缘量子条件相互信息和相对于不同的多分街定义的边缘壁板纠缠与对称性断裂磁体区分拓扑超导体，如比较费米尼克·基塔伊（Fermionic Kitaev）链和spin-1/2 ising模型在横向场中所示。对于具有多个具有不同边缘模式的多个拓扑阶段的系统，例如准1D Kitaev梯子，拓扑壁板纠缠却计算了Majorana激发的数量，并区分了系统的不同拓扑阶段。实际上，我们表明，边缘量子条件互信息和边缘壁板纠缠仍然是拓扑超导的有效检测器，即使对于系统，例如具有长距离跳跃的基塔夫（Kitaev）扎带，具有几何挫败感和被抑制的散装对应关系。
Identifying entanglement-based order parameters characterizing topological systems, in particular topological superconductors and topological insulators, has remained a major challenge for the physics of quantum matter in the last two decades. Here we show that the end-to-end, long-distance, bipartite squashed entanglement between the edges of a many-body system, defined in terms of the edge-to-edge quantum conditional mutual information, is the natural nonlocal order parameter for topological superconductors in one dimension as well as in quasi one-dimensional geometries. For the Kitaev chain in the entire topological phase, the edge squashed entanglement is quantized to log(2)/2, half the maximal Bell-state entanglement, and vanishes in the trivial phase. Such topological squashed entanglement exhibits the correct scaling at the quantum phase transition, is stable in the presence of interactions, and is robust against disorder and local perturbations. Edge quantum conditional mutual information and edge squashed entanglement defined with respect to different multipartitions discriminate topological superconductors from symmetry breaking magnets, as shown by comparing the fermionic Kitaev chain and the spin-1/2 Ising model in transverse field. For systems featuring multiple topological phases with different numbers of edge modes, like the quasi 1D Kitaev ladder, topological squashed entanglement counts the number of Majorana excitations and distinguishes the different topological phases of the system. In fact, we show that the edge quantum conditional mutual information and the edge squashed entanglement remain valid detectors of topological superconductivity even for systems, like the Kitaev tie with long-range hopping, featuring geometrical frustration and a suppressed bulk-edge correspondence.
