Real fermion modes, impurity entropy, and nontrivial fixed points in the phase diagram of junctions of interacting quantum wires and topological superconductors

We discuss how to extend the impurity entropy to systems with boundary interactions depending on zero-mode real fermion operators (Majorana modes as well as Klein factors). As specific applications of our method, we consider a junction between N interacting quantum wires and a topological superconductor, as well as a Y-junction of three spinless interacting quantum wires. In addition we find a remarkable correspondence between the $N=2$ topological superconductor junction and the Y-junction. On one hand, this allows us to determine the range of the system parameters in which a stable phase of the $N=2$ junction is realized as a nontrivial, finite-coupling fixed point corresponding to the M-fixed point in the phase diagram of the Y-junction. On the other hand, it enables us to show the occurrence of a novel "planar" finite-coupling fixed point in the phase diagram of the Y-junction. Eventually, we discuss how to set the system's parameters to realize the correspondence.