Establishing non-Abelian topological order in Gutzwiller-projected Chern insulators via entanglement entropy and modular S-matrix

We use entanglement entropy signatures to establish non-Abelian topological order in projected Chern-insulator wave functions. The simplest instance is obtained by Gutzwiller projecting a filled band with Chern number C = 2, whose wave function may also be viewed as the square of the Slater determinant of a band insulator. We demonstrate that this wave function is captured by the SU(2)(2) Chern-Simons theory coupled to fermions. This is established most persuasively by calculating the modular S-matrix from the candidate ground-state wave functions, following a recent entanglement-entropy-based approach. This directly demonstrates the peculiar non-Abelian braiding statistics of Majorana fermion quasiparticles in this state. We also provide microscopic evidence for the field theoretic generalization, that the Nth power of a Chern number C Slater determinant realizes the topological order of the SU(N)(C) Chern-Simons theory coupled to fermions, by studying the SU(2)(3) (Read-Rezayi-type state) and the SU(3)(2) wave functions. An advantage of our projected Chern-insulator wave functions is the relative ease with which physical properties, such as entanglement entropy and modular S-matrix, can be numerically calculated using Monte Carlo techniques. DOI: 10.1103/PhysRevB.87.161113