The interplay between a topological degeneracy and the residue degeneracy (also known as the residue entropy) of quantum criticality remains an important but not thoroughly understood topic. We find that this topological degeneracy, 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 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 another piece of evidence that can further confirm the existence of a Majorana zero mode.

中文翻译：

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拓扑简并性对耗散共振能级边界Berezinskii-Kosterlitz-Thouless量子相变的影响

量子临界性的拓扑简并性和残差简并性（也称为残差熵）之间的相互作用仍然是一个重要但尚未完全理解的话题。我们发现，这种由马约拉纳零模对提供的拓扑简并性放宽了严格要求的对称性要求，以观察耗散谐振能级的边界 Berezinskii-Kosterlitz-Thouless (BKT) 量子相变 (QPT)。我们的工作表明，拓扑简并性可以被视为实现鲁棒边界 QPT 的辅助对称性。对称性要求的放宽将过渡从一个点延伸到有限区域，从而大大降低了实验观察QPT的难度。另一方面，这种涉及拓扑的奇异 BKT 相图提供了另一个证据，可以进一步证实马约拉纳零模式的存在。