标题： 交替自旋链中拓扑边缘态对环境的鲁棒性 显示英文标题

标题： Robustness of topological edge states in alternating spin chains against environment

摘要： 具有 Haldane 自旋-$1$链和自旋-$1/2$的二聚链都表现出拓扑保护的边缘态，并且这些边缘态对特定扰动具有鲁棒性。最近，这类自旋链已被专门组装在表面上，我们在这里研究了这些边缘态在与表面耦合时的鲁棒性。由于没有任何物理系统可以被认为是完全隔离的，因此检查在环境耦合存在的情况下拓扑鲁棒性是否得以维持至关重要。我们通过对基于自旋-$1/2$的交替海森堡自旋链应用精确对角化方法来求解一个与表面通过各种跃迁算符耦合的林德布拉德主方程。拓扑态的鲁棒性通过基态简并度、相关函数、熵以及边缘态磁化的时域演化来评估。我们研究了由反铁磁和铁磁内二聚体耦合组成的链，类似于 Su-Schrieffer-Heeger 和 Haldane 模型，并评估了$z$轴各向异性和更长范围耦合的影响。总体而言，我们发现 Su-Schrieffer-Heeger 类似链中的拓扑性质比 Haldane 类似链中的更为稳健。 显示英文摘要

摘要： Both the Haldane spin-$1$ chain and dimerized chains of spin-$1/2$ exhibit topologically protected edge states that are robust against specific perturbations. Recently, such spin chains have been specifically assembled on surfaces and we investigate here the robustness of these edge states against coupling to the surface. Since no physical system can be considered perfectly isolated, it is crucial to examine whether topological robustness is maintained in the presence of environmental coupling. We apply exact diagonalization to a Lindblad master equation that couples an alternating Heisenberg spin chain based on spins $1/2$ to a surface via various jump operators. The robustness of topological states is assessed via the time evolution of quantities such as the ground-state degeneracy, correlation function, entropy, and magnetization of edge states. We investigate chains built from dimers with antiferromagnetic and ferromagnetic intra-dimer coupling, which resemble Su-Schrieffer-Heeger and the Haldane models, resp., and assess the impact of $z$-axis anisotropy and longer-ranged couplings. Generally, we find that signatures of topological properties are more robust in Su-Schrieffer-Heeger-like chains than in Haldane-like chains.