长程相互作用下带隙外尔半金属费米弧态的命运
Fate of Fermi-arc States in Gapped Weyl Semimetals under Long-ranged Interactions
摘要：
对于非相互作用的外尔半金属，当体单粒子能谱中存在无带隙外尔节点时，费米弧表面态可以产生。然而，在存在电子相关性的情况下，不清楚这种体边界对应是否仍然成立。最近，新的关联相预计将出现在WSM与长程相互作用，其中体Weyl节点可以缺口，但不破坏其拓扑性质。在这里，我们探讨的费米弧状态的影响下，这种长程相互作用的命运。映射到一个一维的相互作用的苏-Schrieffer-Heeger（SSH）模型与两个开放端的系统后，我们采用数值精确对角化来解决的问题是否费米弧状态将被修改。通过将我们的数据外推到热力学极限，我们发现对于那些给出非相互作用费米弧态的动量，相应SSH模型的零能边缘态仍然存在。此外，这一观察适用于单粒子和集体边缘激发。由于这些边缘态的轨迹构成费米弧，因此证明了费米弧态对长程相互作用的鲁棒性。特别是单粒子性质的费米弧，即使外尔节点处的单粒子能隙因相互作用而打开，也能继续存在。我们的结果说明了微妙的相互作用WSM的拓扑相位识别和显示的局限性的方法简单地通过检查单粒子谱的节点结构。
英文摘要：
For noninteracting Weyl semimetals (WSMs), Fermi-arc surface states can arise when there exist gapless Weyl nodes in the bulk single-particle spectrum. However, in the presence of electronic correlations, it is not clear whether this bulk-boundary correspondence still holds or not. Recently, novel correlated phases are predicted to appear in WSMs with long-ranged interactions, in which the bulk Weyl nodes can be gapped but without destroying their topological properties. Here, we explore the fate of the Fermi-arc states under the influence of such long-ranged interactions. After mapping the system onto a one-dimensional interacting Su-Schrieffer-Heeger (SSH) model with two open ends, we employ numerical exact diagonalizations to address the issue whether the Fermi-arc states will be modified. By extrapolating our data to the thermodynamic limit, we find that the zero-energy edge states of the corresponding SSH model still exist for those momenta giving the noninteracting Fermi-arc states. Moreover, this observation applies to both the single-particle and the collective edge excitations. Since the locus of these edge states constitutes the Fermi arcs, the robustness of the Fermi-arc states against long-ranged interactions is thus demonstrated. In particular, the Fermi arcs of single-particle nature can survive even when the single-particle gaps at the Weyl nodes are opened by interactions. Our results illustrate the subtlety in identifying the topological phases of interacting WSMs and show the limitation of the approaches simply by examining the nodal structure of the single-particle spectrum.
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