Abstract
We demonstrate how to directly study non-Abelian statistics for a wide class of exactly solvable many-body quantum systems. By employing exact eigenstates to simulate the adiabatic transport of a model's quasi-particles, the resulting Berry phase provides a direct demonstration of their non-Abelian statistics. We apply this technique to Kitaev's honeycomb lattice model and explicitly demonstrate the existence of non-Abelian Ising anyons confirming the previous conjectures. Finally, we present the manipulations needed to transport and detect the statistics of these quasi-particles in the laboratory. Various physically realistic system sizes are considered and exact predictions for such experiments are provided.
Highlights
A striking feature of topological phases of matter is that they can support anyons
Other proposals include the p-wave superconductor [5, 6] as well as various lattice models [7, 8, 9]. These systems are either tailored to identically support non-Abelian statistics and have complex physical realizations, or they can be described by simple Hamiltonians, but their statistical behavior is based on indirect arguments
When the positions are swapped twice, i.e. a particle winds around the other along a suitable chosen path, the statistics corresponds to the accumulated wave function evolution, which is given by the Berry phase, or the holonomy [10, 16]
Summary
A striking feature of topological phases of matter is that they can support anyons. These are quasiparticles with statistics different from bosons or fermions. Other proposals include the p-wave superconductor [5, 6] as well as various lattice models [7, 8, 9] These systems are either tailored to identically support non-Abelian statistics and have complex physical realizations, or they can be described by simple Hamiltonians, but their statistical behavior is based on indirect arguments. By applying the Berry phase technique [10] to the Kitaev’s honeycomb spin lattice model [9], we calculate the evolution associated with an adiabatic exchange of quasiparticles. This is performed using exact eigenstates of a 360 spin system.
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