论文标题
多政治一维拓扑绝缘子中的缩放行为
Scaling behavior in a multicritical one-dimensional topological insulator
论文作者
论文摘要
一类自旋轨耦合电子的Aubry-André-Harper模型表现出拓扑相图，其中属于同一相的两个区域被多个智力点拆分。此时满足的临界线定义了地面能量的二阶非分析性的拓扑量子相变，并伴随着光谱间隙相对于控制参数的线性闭合；除了在多政治点上支持抛物线差距的四阶转变。这里通过对模型拓扑不变定义的曲率函数的缩放分析来表征两种类型的临界性。我们在缝隙关闭的Brillouin区域的非高对称点处提取分解曲率函数的临界指数，并在高对称点处采用重新归一化组方法来实现平坦的曲率函数。我们还得出了Wannier状态之间与基础无关的相关函数，以表征过渡。有趣的是，我们发现，无论过渡的顺序如何，相对于光谱差距定义的临界指数和缩放定律仍然相同。
A class of Aubry-André-Harper models of spin-orbit coupled electrons exhibits a topological phase diagram where two regions belonging to the same phase are split up by a multicritical point. The critical lines which meet at this point each defines a topological quantum phase transition with a second-order nonanalyticity of the ground-state energy, accompanied by a linear closing of the spectral gap with respect to the control parameter; except at the multicritical point which supports fourth-order transitions with parabolic gap-closing. Here both types of criticality are characterized through a scaling analysis of the curvature function defined from the topological invariant of the model. We extract the critical exponents of the diverging curvature function at the non-high symmetry points in the Brillouin zone where the gap closes, and also apply a renormalization group approach to the flattening curvature function at high symmetry points. We also derive a basis-independent correlation function between Wannier states to characterize the transition. Intriguingly, we find that the critical exponents and scaling law defined with respect to the spectral gap remain the same regardless of the order of the transition.
