  We consider a helical spin liquid system which shows majorana fermion modes
at the edge. The interaction between the quasiparticles in this system induces
phase transition, Majorana-Ising transition. We comply the density matrix
renormalization group method to study this phase transition for the entire
regime of the parameter space. We observe the presence of topological quantum
phase transition for repulsive interaction, however this phase is more stable
for the attractive interaction. The length scale dependent study shows many new
and important results and we show explicitly that the major contribution to the
excitation comes from the edge of the system when the system is in the
topological state. We also show the dependence of Majorana localization length
for various values of chemical potential.
