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.

arXiv comment5 pages and 2 figures

References in corpus (27)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Topological quantum memory
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Fractional quantum Hall states at zero magnetic field
• Topological orders and Edge excitations in FQH states
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Fractional quantum Hall effect in the absence of Landau levels
• Fractional Chern Insulator
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Fractional Quantum Hall Effect of Hard-Core Bosons in Topological Flat Bands
• Topological Entanglement Entropy in Chern-Simons Theories and Quantum Hall Fluids
• Topological flat band models with arbitrary Chern numbers
• Emergent Many-Body Translational Symmetries of Abelian and Non-Abelian Fractionally Filled Topological Insulators
• Entanglement entropy of critical spin liquids
• Non-Abelian Quantum Hall Effect in Topological Flat Bands
• Projective Construction of Non-Abelian Quantum Hall Liquids
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Fractionalization, topological order, and quasiparticle statistics
• Topological Entanglement Entropy of Z2 Spin liquids and Lattice Laughlin states
• Fractional quantum-Hall liquid spontaneously generated by strongly correlated t_2g electrons
• Symmetry protected fractional Chern insulators and fractional topological insulators
• Effective Field Theory and Projective Construction for the Z_k Parafermion Fractional Quantum Hall States
• Fractional spin liquid hierarchy for spin S antiferromagnets

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• Topological Flat Band Models and Fractional Chern Insulators
• Fractional Quantum Hall Physics in Topological Flat Bands
• Topological quasiparticles and the holographic bulk-edge relation in 2+1D string-net models
• Edge theory approach to topological entanglement entropy, mutual information and entanglement negativity in Chern-Simons theories
• Momentum polarization: an entanglement measure of topological spin and chiral central charge
• Parton construction of a wave function in the anti-Pfaffian phase
• Variational Monte Carlo study of chiral spin liquid in the extended Heisenberg model on the Kagome lattice
• Fibonacci Anyons From Abelian Bilayer Quantum Hall States
• Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice
• Chiral spin liquids in triangular lattice SU(N) fermionic Mott insulators with artificial gauge fields
• Chiral spin density wave, spin-charge-Chern liquid and d+id superconductivity in 1/4-doped correlated electronic systems on the honeycomb lattice
• Local Kekulé distortion turns twisted bilayer graphene into topological Mott insulators and superconductors
• Identifying Non-Abelian Topological Order through Minimal Entangled States
• General procedure for determining braiding and statistics of anyons using entanglement interferometry
• Fractional Chiral Hinge Insulator
• Topological Characterization of Non-Abelian Moore-Read State using Density-Matrix Renormailzation Group
• Edge Excitations in Fractional Chern Insulators
• Wave Functions for Fractional Chern Insulators on Disk Geometry
• Possible non-Abelian Moore-Read state in double-layer bosonic fractional quantum Hall system
• Identifying non-Abelian topological ordered state and transition by momentum polarization
• Symmetry Fractionalized (Irrationalized) Fusion Rules and Two Domain-Wall Verlinde Formulae
• Fermionic tensor networks for higher order topological insulators from charge pumping
• Classification and emergence of quantum spin liquids in chiral Rydberg models
• Invariance of topological indices under Hilbert space truncation
• 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
• Non-Abelian topological order with SO(5)${}_1$ chiral edge states