Non-Abelian fractional Chern insulator in disk geometry

Abstract

Non-Abelian (NA) fractional topological states with quasi-particles obeying NA braiding statistics have attracted intensive attentions for both its fundamental nature and the prospect for topological quantum computation. To date, there are many models proposed to realize the NA fractional topological states, such as the well-known Moore-Read quantum Hall states and the Non-Abelian fractional Chern insulators (NA-FCIs). Here, we investigate the NA-FCI in disk geometry with three-body hard-core bosons loaded into a topological flat band. This stable ν = 1 bosonic NA-FCI is characterized by the edge excitations and the ground-state angular momentum. Based on the generalized Pauli principle and the Jack polynomials, we successfully construct a trial wave function for the NA-FCI. Moreover, a ν = 1/2 Abelian FCI state emerges with the increase of the on-site interaction and it can be identified with the help of the trial wave function as well. Our findings not only lead to an optimal wave function for the NA-FCI, but also directly provide an effective approach for future researches on paired topological states.

Recent Developments in Fractional Chern Insulators

“…Moreover, the entanglement spectrum (ES) [97] of the ground state, i.e., the whole spectrum of the reduced density matrix of one subsystem, contains more information than the entanglement entropy. For the real-space bipartition, the counting structure in the low-lying ES [78,95,96,[98][99][100][101][102] is the same as that of edge excitations [103][104][105], thus providing a fingerprint of the underlying topological order according to the bulk-edge correspondence.…”