Inter-edge interactions and novel fixed points at a junction of quantum Hall line junctions

We investigate novel fixed points characterized by matrices specifying the splitting of currents at a junction of three quantum Hall line junctions. In this study, we find that for a junction of fractional quantum Hall edge states, both flower (single droplet) and islands (three droplets) configurations are stable in an intermediate region across a range of inter-edge repulsive interactions. Additionally, we analyze how a measurement of the tunneling conductance as a function of the gate voltage, which controls inter-edge repulsions, can provide clear experimental signals of this stability region. The impact of the geometry of the quantum Hall droplet and the tunneling locations on transport is highlighted, offering insights into the tunability of interactions between chiral edge states. This work contributes to the understanding of one-dimensional systems of interacting electrons and their applications in condensed matter physics.