Abstract
Strongly interacting topologically ordered many-body systems consisting of fermions or bosons can host exotic quasiparticles with anyonic statistics. This raises the question whether many-body systems of anyons can also form anyonic quasiparticles. Here, we show that one can, indeed, construct many-anyon wavefunctions with anyonic quasiparticles. The braiding statistics of the emergent anyons are different from those of the original anyons. We investigate hole type and particle type anyonic quasiparticles in Abelian systems on a two-dimensional lattice and compute the density profiles and braiding properties of the emergent anyons by employing Monte Carlo simulations.
Highlights
Quantum statistics is an important concept for gaining insight into numerous observed collective phenomena in nature
One can approach the continuum limit by increasing the number of lattice sites, and in this limit the wave function coincides with one of the states in the lowest Landau level ground state basis of the many-anyon continuum Hamiltonian studied in Ref. [17]
We have shown that systems consisting of many anyons can support the formation of anyonic quasiparticles and that the braiding properties of the emergent anyons can differ from the properties of the original anyons
Summary
Quantum statistics is an important concept for gaining insight into numerous observed collective phenomena in nature. Instead of studying systems with isolated anyonic excitations, one can study systems with many anyons Such ideas have, e.g., been used in Haldane’s hierarchy construction [13] to propose trial states for fractional quantum Hall systems at Landau-level filling fractions other than 1/3, e.g., 2/5 and 2/7. One can obtain the exact ground-state basis for such a continuum many-anyon Hamiltonian, which is entirely confined to the lowest Landau level [16,17,18]. One can approach the continuum limit by increasing the number of lattice sites, and in this limit the wave function coincides with one of the states in the lowest Landau level ground state basis of the many-anyon continuum Hamiltonian studied in Ref. One can physically realize the lattice wave function by realizing this Hamiltonian
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