Exact solutions of a model for synthetic anyons in a noninteracting system

Abstract

Synthetic anyons can be implemented in a noninteracting many-body system, by using specially tailored localized (physical) probes, which supply the demanded nontrivial topology in the system. We consider the Hamiltonian for noninteracting electrons in two-dimensions (2D), in a uniform magnetic field, where the probes are external solenoids with a magnetic flux that is a fraction of the flux quantum. The Hamiltonian could also be implemented in an ultracold (fermionic) atomic gas in 2D, in a uniform synthetic magnetic field, where the probes are lasers giving rise to synthetic solenoid gauge potentials. We find analytically and numerically the ground state of this system when only the lowest Landau level states are occupied. It is shown that the ground state is anyonic in the coordinates of the probes. We show that these synthetic anyons cannot be considered as emergent quasiparticles. The fusion rules of synthetic anyons are discussed for different microscopic realizations of the fusion process.

An exactly solvable model for anyons with non-Abelian flux

“…In comparison to the system studied in Ref. [38], the novel ingredient here is that the vector potential of the solenoids is non-Abelian. We write it in the form…”

“…This problem was studied in Ref. [38] (see the Appendix of that paper for details of calculation), we only briefly outline the key steps leading to the solution. First of all, let us consider a single particle (N e = 1) solution of Eq.…”

“…It should be pointed out that these synthetic Abelian anyons are not emergent quasiparticles (see Refs. [38,39] and the commentary on Refs. [31,32] therein)…”

“…In this regard, anyons were proposed to be realized in a system of an artificially structured type-II superconducting film [31,32] adjacent to a 2D electron gas (2DEG) in the Integer Quantum Hall Effect (IQHE) [33,34], in IQHE magnets [35], in topological defects in graphene [36], and by sandwiching a charged magnetic dipole between two semi-infinite blocks of a high permeability metamaterial [37]. Recently, a theoretical model for synthetic Abelian anyons in a noninteracting system was proposed along these lines [38], in which specially tailored localized probes are brought into the IQHE setup and shown to have anyonic properties. It should be pointed out that these synthetic Abelian anyons are not emergent quasiparticles (see Refs.…”

“…In this paper we follow the aforementioned model [38] and generalize it in two aspects. First, we introduce the spin interaction between the electrons in such a way to produce a degenerate ground state, the arena for non-Abelian physics, and second, we equip the probes with a non-Abelian gauge potential.…”