标题： 拓扑非平凡的多临界点 显示英文标题

标题： Topologically nontrivial multicritical points

摘要： 最近，一维拓扑链中拓扑与量子临界性的有趣相互作用被揭示出来，这些链具有扩展的最近邻耦合。 在这些系统中，尽管体能隙消失，但会出现具有局域化边缘模式的拓扑不同的临界相。 在本工作中，我们研究了不同带隙和临界相交汇的拓扑多临界点。 具体来说，我们考虑了一个耦合到第三近邻的拓扑链，该链在多临界点表现出稳定的局域化边缘模式。 这些点仅在其周围具有非平凡的带隙和临界相，并且还由能隙闭合点附近的二次色散所表征。 我们通过从与哈密顿量相关的复函数的零点获得的拓扑不变量来表征拓扑多临界点。 此外，我们通过计算相关多项式的判别式来分析多临界点附近的零点性质。 判别式唯一地识别出拓扑多临界点，并将它们与平凡点区分开来。 我们最后研究了弱无序强度下多临界点处零能模的鲁棒性，并揭示了在强无序强度下存在一个拓扑非平凡的无隙安德森局域相。 显示英文摘要

摘要： Recently, the intriguing interplay between topology and quantum criticality has been unveiled in one-dimensional topological chains with extended nearest-neighbor couplings. In these systems, topologically distinct critical phases emerge with localized edge modes despite the vanishing bulk gap. In this work, we study the topological multicritical points at which distinct gapped and critical phases intersect. Specifically, we consider a topological chain with coupling up to the third nearest neighbors, which shows stable localized edge modes at the multicritical points. These points possess only nontrivial gapped and critical phases around them and are also characterized by the quadratic dispersion around the gap-closing points. We characterize the topological multicritical points in terms of the topological invariant obtained from the zeros of the complex function associated with the Hamiltonian. Further, we analyze the nature of zeros in the vicinity of the multicritical points by calculating the discriminants of the associated polynomial. The discriminant uniquely identifies the topological multicritical points and distinguishes them from the trivial ones. We finally study the robustness of the zero-energy modes at the multicritical points at weak disorder strengths, and reveal the presence of a topologically nontrivial gapless Anderson-localized phase at strong disorder strengths.