Kumar Ranjith R, Kartik Y R, Rahul S, Sarkar Sujit
Department of Theoretical Sciences, Poornaprajna Institute of Scientific Research, 4, Sadashivanagar, Bangalore, 560 080, India.
Graduate Studies, Manipal Academy of Higher Education, Madhava Nagar, Manipal, 576104, India.
Sci Rep. 2021 Jan 13;11(1):1004. doi: 10.1038/s41598-020-80337-7.
The investigation and characterization of topological quantum phase transition between gapless phases is one of the recent interest of research in topological states of matter. We consider transverse field Ising model with three spin interaction in one dimension and observe a topological transition between gapless phases on one of the critical lines of this model. We study the distinct nature of these gapless phases and show that they belong to different universality classes. The topological invariant number (winding number) characterize different topological phases for the different regime of parameter space. We observe the evidence of two multi-critical points, one is topologically trivial and the other one is topologically active. Topological quantum phase transition between the gapless phases on the critical line occurs through the non-trivial multi-critical point in the Lifshitz universality class. We calculate and analyze the behavior of Wannier state correlation function close to the multi-critical point and confirm the topological transition between gapless phases. We show the breakdown of Lorentz invariance at this multi-critical point through the energy dispersion analysis. We also show that the scaling theories and curvature function renormalization group can also be effectively used to understand the topological quantum phase transitions between gapless phases. The model Hamiltonian which we study is more applicable for the system with gapless excitations, where the conventional concept of topological quantum phase transition fails.
无隙相之间拓扑量子相变的研究与表征是近期拓扑物态研究的热点之一。我们考虑一维具有三自旋相互作用的横场伊辛模型，并在该模型的一条临界线上观测到了无隙相之间的拓扑相变。我们研究了这些无隙相的不同性质，并表明它们属于不同的普适类。拓扑不变数（缠绕数）在参数空间的不同区域表征不同的拓扑相。我们观测到了两个多临界点的证据，一个是拓扑平凡的，另一个是拓扑活跃的。临界线上无隙相之间的拓扑量子相变通过里夫希茨普适类中的非平凡多临界点发生。我们计算并分析了接近多临界点时的万尼尔态关联函数的行为，并证实了无隙相之间的拓扑相变。通过能量色散分析，我们展示了在这个多临界点处洛伦兹不变性的破缺。我们还表明，标度理论和曲率函数重整化群也能有效地用于理解无隙相之间的拓扑量子相变。我们所研究的模型哈密顿量更适用于具有无隙激发的系统，在这类系统中传统的拓扑量子相变概念失效。
