Fibonacci anyon excitations of one-dimensional dipolar lattice bosons

TL;DR

This paper investigates a one-dimensional dipolar boson system, revealing conditions for Fibonacci anyon excitations with implications for topological quantum computing, and clarifies phase transitions excluding super-solid phases at specific fillings.

Contribution

It identifies parameter regimes supporting Fibonacci anyon excitations in 1D dipolar bosons and clarifies the phase diagram, excluding super-solid phases at 3/2 filling.

Findings

Fibonacci anyon excitations occur at specific parameters.

Super-solid phases are absent at 3/2 filling.

A direct BKT transition from superfluid to charge-density wave is observed.

Abstract

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.