Emergence of different interesting and insightful phenomena in different length scales is the heart of quantum many-body system. We present emergence of quantum phases for the interacting helical liquid of topological quantum matter. We also observe that Luttinger liquid parameter plays a significant role to determine different quantum phases. We use three sets of renormalisation group (RG) equations to solve emergent quantum phases for our model Hamiltonian system. Two of them are the quantum Berezinskii–Kosterlitz–Thouless (BKT) equations. We show explicitly from the study of length scale-dependent emergent physics that there is no evidence of Majorana–Ising transition for the two sets of quantum BKT equations, i.e., the system is either in the topological superconducting phase or in the Ising phase. The whole set of RG equation shows the evidence of length scale-dependent Majorana–Ising transition. Emergence of length scale-dependent quantum phases can be observed in topological materials which exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology.
Volume 96, 2022
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