Influence of Majorana-parity degeneracy on the boundary Berezinskii-Kosterlitz-Thouless quantum phase transition of a dissipative resonant level

The interplay between a topological degeneracy and the residue degeneracy (also known as the residue entropy) of quantum criticality remains as an important but not thoroughly understood topic. We find that the degeneracy of topological parity, provided by a Majorana zero mode pair, relaxes the otherwise strictly requested symmetry requirement, to observe the boundary Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition (QPT) of a dissipative resonant level. Our work indicates that the topological-parity degeneracy can be potentially viewed as an auxiliary symmetry that realizes a robust boundary QPT. The relaxation of the symmetry requirement extends the transition from a point to a finite area, thus greatly reducing the difficulty to experimentally observe the QPT. This topology-involved exotic BKT phase diagram, on the other hand, provides a piece of convincing evidence for a Majorana zero mode.