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

## TL;DR

This paper extends impurity entropy concepts to systems with boundary zero-mode fermions, analyzing junctions of quantum wires and topological superconductors, revealing new fixed points and phase diagram correspondences.

## Contribution

It introduces a method to compute impurity entropy with boundary Majorana modes and uncovers novel fixed points in quantum wire junction phase diagrams.

## Key findings

- Identification of a stable nontrivial fixed point in the N=2 topological superconductor junction.
- Discovery of a new 'planar' finite-coupling fixed point in the Y-junction phase diagram.
- Establishment of a correspondence between N=2 superconductor junctions and Y-junctions.

## Abstract

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.