AI 中文总结
采用曲率重整化群方法，研究周期跳跃调制的SSH链的拓扑相变，发现不同临界点的曲率函数发散特性不同，对应不同普适类，边缘态衰减速度也存在差异。
AI 中文摘要
我们采用曲率重整化群（CRG）方法研究Su-Schrieffer-Heeger（SSH）链及其受周期跳跃调制的扩展模型中的拓扑相变。在高对称点附近，我们根据系统参数定义曲率函数，该函数在临界点处的发散与普通相变类似，标志着拓扑相变的发生。根据该理论，两格点SSH模型的相变线出现在Δ=0的临界线上，此时曲率函数发散。我们的研究涵盖该模型以及周期为4个晶格间距的调制模型，对于后者，曲率函数不仅在类狄拉克拓扑相变点|Δ/t|=√2处发散，还在非拓扑无能隙点Δ=0处呈现更快的发散。我们进一步注意到，当Δ→0时，关联长度的发散速度比|Δ/t|→√2时更快，这导致两组不同的临界指数，使它们属于不同的普适类。在Δ=0点附近，边缘态向体内的衰减非常缓慢，而在|Δ/t|=√2点附近，可观察到边缘态向体内的衰减速度快得多。我们还对跳跃周期为8个晶格间距的SSH模型开展了类似分析。
英文摘要
We use a curvature renormalization group (CRG) approach to study the topological phase transitions in a Su-Schrieffer-Heeger chain and its extensions coming from periodic hopping modulations. A curvature function is defined in terms of system parameters near high-symmetry points where the divergence of this function at critical points, in analogy to usual phase transitions, signals a topological phase transition. According to this theory, the phase transition line for the two-site Su-Schrieffer-Heeger (SSH) model is visible at the critical line Δ= 0 where the curvature function diverges. Our study involves this model and also the modulated one with periodicity of four lattice spacing where the curvature function not only diverges at the topological phase transition point (Dirac-like) |Δ/t| = \sqrt(2) but also shows faster divergence at the non-topological gapless point Δ= 0. We further notice faster divergence of correlation length for Δ-> 0 as compared to that for the |Δ/t| -> \sqrt(2) resulting in two different sets of critical exponents making them lie in different universality classes. The edge state exhibits very slow decay into the bulk near the Δ= 0 point while a much quicker decay from edge into bulk is discernible around the |Δ/t| = \sqrt(2) point. We also continue similar analysis for a SSH model with hopping periodicity of eight lattice spacing.
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