Establishing non-Abelian topological order in Gutzwiller projected Chern insulators via Entanglement Entropy and Modular S-matrix

Abstract

We use entanglement entropy signatures to establish non-Abelian topological order in projected Chern-insulator wavefunctions. The simplest instance is obtained by Gutzwiller projecting a filled band with Chern number C=2, whose wavefunction may also be viewed as the square of the Slater determinant of a band insulator. We demonstrate that this wavefunction 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 wavefunctions, 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 $SU(3{)}_2$ wavefunctions. An advantage of our projected Chern insulator wavefunctions is the relative ease with which physical properties, such as entanglement entropy and modular S-matrix can be numerically calculated using Monte Carlo techniques.

5 pages and 2 figures

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• Symmetry Fractionalized (Irrationalized) Fusion Rules and Two Domain-Wall Verlinde Formulae
• Classification and emergence of quantum spin liquids in chiral Rydberg models
• Detecting topological order from modular transformations of ground states on the torus
• Recent progress in quantum spin liquids, fractional magnetization plateaus, and unconventional superconductivity in kagome lattices
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