论文标题
远程自由阵容连锁店中的散装对应关系和奇异性填充
Bulk-boundary correspondence and singularity-filling in long-range free-fermion chains
论文作者
论文摘要
散装的对应关系将受拓扑保护的边缘模式与散装拓扑结合起来，并且对短距离自由陶瓷链充分理解。尽管案例研究考虑了远程哈密顿量，其耦合与幂律指数$α$衰减，但没有针对自由屈服的对称类别进行系统的研究。我们引入了一种技术，用于在1D BDI和AIII对称类中求解带有$α> 1 $的AIII对称性类别的技术，将量化的绕组不变的，散装式拓扑排序参数和边缘模式的完整解决方案链接在一起。通过研究由哈密顿量的耦合确定的复杂函数来阐明这些链的物理学：与边缘模式与该功能的根相关的短距离情况相反，我们发现它们现在与奇异性相关。一个显着的结果是，边缘模式的有限尺寸分裂取决于拓扑绕组数，可以用作后者的探针。此外，我们通过（i）确定$α<1 $仍然存在的BDI链的家族来概括这些结果，并且（ii）表明，当$α-1 $ $α-1 $超过动态关键指数时，无质子对称性拓扑链可以具有拓扑不变性和边缘模式。
The bulk-boundary correspondence relates topologically-protected edge modes to bulk topological invariants, and is well-understood for short-range free-fermion chains. Although case studies have considered long-range Hamiltonians whose couplings decay with a power-law exponent $α$, there has been no systematic study for a free-fermion symmetry class. We introduce a technique for solving gapped, translationally invariant models in the 1D BDI and AIII symmetry classes with $α>1$, linking together the quantized winding invariant, bulk topological string-order parameters and a complete solution of the edge modes. The physics of these chains is elucidated by studying a complex function determined by the couplings of the Hamiltonian: in contrast to the short-range case where edge modes are associated to roots of this function, we find that they are now associated to singularities. A remarkable consequence is that the finite-size splitting of the edge modes depends on the topological winding number, which can be used as a probe of the latter. We furthermore generalise these results by (i) identifying a family of BDI chains with $α<1$ where our results still hold, and (ii) showing that gapless symmetry-protected topological chains can have topological invariants and edge modes when $α-1$ exceeds the dynamical critical exponent.
