Minimal Entangled States and Modular Matrix for Fractional Quantum Hall Effect in Topological Flat Bands

Abstract

We perform an exact diagonalization study of the topological order in topological flat band models through calculating entanglement entropy and spectra of low energy states. We identify multiple independent minimal entangled states, which form a set of orthogonal basis states for the ground-state manifold. We extract the modular transformation matrices S (U) which contains the information of mutual (self) statistics, quantum dimensions and fusion rule of quasi-particles. Moreover, we demonstrate that these matrices are robust and universal in the whole topological phase against different perturbations until the quantum phase transition takes place.

References in corpus (13)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• Identifying Topological Order by Entanglement Entropy
• Characterizing topological order by studying the ground states of an infinite cylinder
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
• Topological Entanglement Entropy from the Holographic Partition Function
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• From fractional Chern insulators to Abelian and non-Abelian fractional quantum Hall states: adiabatic continuity and orbital entanglement spectrum
• Quantum phases of disordered flatband lattice fractional quantum Hall systems

Cited by in corpus (33)

• Topological Flat Band Models and Fractional Chern Insulators
• Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
• Dynamical Time-Reversal Symmetry Breaking and Photo-Induced Chiral Spin Liquids in Frustrated Mott Insulators
• Characterization and stability of a fermionic ν=1/3 fractional Chern insulator
• Twisted Injectivity in PEPS and the Classification of Quantum Phases
• Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid
• Numerical study of a transition between Z2 topologically ordered phases
• Obtaining topological degenerate ground states by the density matrix renormalization group
• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
• Detection of Symmetry Enriched Topological Phases
• Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids
• Recent Developments in Fractional Chern Insulators
• Identifying Non-Abelian Topological Order through Minimal Entangled States
• Interaction-driven fractional quantum Hall state of hard-core bosons on kagome lattice at one-third filling
• General procedure for determining braiding and statistics of anyons using entanglement interferometry
• Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands
• Topological Characterization of Non-Abelian Moore-Read State using Density-Matrix Renormailzation Group
• Modular matrices from universal wave function overlaps in Gutzwiller-projected parton wave functions
• Intrinsic sign problems in topological quantum field theories
• Robustness of Topological Order in the Toric Code with Open Boundaries
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Wave Functions for Fractional Chern Insulators on Disk Geometry
• Evolution of quantum entanglement with disorder in fractional quantum Hall liquids
• Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at $m=\frac{2}{3}$ magnetization
• Possible non-Abelian Moore-Read state in double-layer bosonic fractional quantum Hall system
• An Operational Definition of Topological Order
• Spin, orbital and topological order in models of strongly correlated electrons
• Microscopic Diagnosis of Universal Geometric Responses in Fractional Quantum Hall Liquids
• Full characterization of a spin liquid phase: from topological entropy to robustness and braid statistics
• Topological Minimally Entangled States via Geometric Measure
• Transition of a ${\mathbb{Z}}_3$ topologically ordered phase to trivial and critical phases
• Fractional quantum Hall states with gapped boundaries in an extreme lattice limit
• Optical Signature of Flat Bands in Topological Hourglass Semimetal Nb3SiTe6