Fibonacci anyon excitations of one-dimensional dipolar lattice bosons

We study a system of dipolar bosons in a one-dimensional optical lattice using exact diagonalization and density matrix renormalization group methods. In particular, we analyze low energy properties of the system at an average filling of 3/2 atoms per lattice site. We identify the region of the parameter space where the system has non-Abelian Fibonacci anyon excitations that correspond to fractional domain walls between different charge-density-waves. When such one-dimensional systems are combined into a two-dimensional network, braiding of Fibonacci anyon excitations has potential application for fault tolerant, universal, topological quantum computation. Contrary to previous calculations, our results also demonstrate that super-solid phases are not present in the phase diagram for the discussed 3/2 average filling. Instead, decreasing the value of the nearest-neighbor tunneling strength leads to a direct, Berezinskii-Kosterlitz-Thouless, super-fluid to charge-density-wave quantum phase transition.