  We present results for asymptotic freedom like behavior for the topological
state of the helical spin liquid system with finite proximity induced
superconducting gap. We derive two different quantum
Berezinskii-Kosterlitz-Thouless (BKT) equations for the two different limit of
this model Hamiltonian. The common quantum phase for these two quantum BKT
transitions is the helical Luttinger liquid phase where there is no evidence of
asymptotic freedom. There is no evidence of superconductor-insulator transition
for this asymptotic freedom study. We observe the evidance of asymptotic
freedom for the two model Hamiltonian, but the character of the asymptotic
phases are different. We also observe that the Luttinger liquid parameter plays
a significant role to determine the asymptotic freedom but the chemical
potential has no effect on it.
