Quantum Berezinskii–Kosterltz–Thouless transition for topological insulator

Abstract

We present extensive calculation and the results of quantum Berezinskii-Kosterlitz-Thouless (BKT) transition for interacting helical liquid system. This system shows the quantum BKT transition for the different physical situation which we present by two model Hamiltonians. We derive the renormalization group (RG) equations explicitly and present the flow lines behavior. We also present RG flow lines based on the exact solution. We observe that the Majorana fermion zero modes physics and the gapped Ising phase of the system. We also observe that the evidence of gapless Luttinger liquid phase as a common phase for both quantum BKT transitions.

Topological quantum phase transitions and criticality in a longer-range Kitaev chain

“…This insight helped scientific community to think about topological state of matter from the perspective of criticality. Even earlier there were many attempts like renormalization group [13][14][15], curvature function renormalization group [16] and other scaling approaches to explain TQPT [17,18]. But now it is evident that there is a possibility to explain criticality through correlation function, curvature function [16], critical exponents, and universality class of TQPT [11,12].…”

Topological quantum phase transitions and criticality in a longer-range Kitaev chain

“…This insight helped scientific community to think about topological state of matter from the perspective of criticality. Even earlier, there were many attempts like renormalization group [12][13][14] , curvature function renormalization group 15 and other scaling approaches to explain TQPT 16,17 . But now it is evident that, there is a possibility to explain criticality through correlation function, curvature function 15 , critical exponents and universality class of TQPT 11,18 .…”