A Study of Asymptotic Freedom like Behavior for Topological States of Matter

TL;DR

This paper investigates asymptotic freedom-like behavior in topological helical spin liquids with superconducting gaps, deriving BKT equations and analyzing phase transitions and parameters influencing asymptotic phases.

Contribution

It introduces two quantum BKT equations for different limits of a topological model and explores conditions for asymptotic freedom in helical spin liquids.

Findings

Asymptotic freedom observed in two model Hamiltonians.

Luttinger liquid parameter influences asymptotic behavior.

Chemical potential does not affect asymptotic freedom.

Abstract

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.