The next-next-nearest neighbor interaction of two Fibonacci anyons

The interaction between the next-next-nearest neighboring Fibonacci anyons was observed. The union requires the greatest proximity between the particles, hence the need for two braiding processes. The outcome of the fusion is projected onto the trivial channel, to signify a preference to the ferromagnetic state (i.e., having a negative coupling strength constant). The next-next-nearest neighbor interaction is shown to be more favorable than the next-nearest neighbor interaction.