Fractionalization, topological order, and quasiparticle statistics

Abstract

We argue, based on general principles, that topological order is essential to realize fractionalization in gapped insulating phases in dimensions $d\ge 2$. In $d=2$ with genus $g$, we derive the existence of the minimum topological degeneracy $q^g$ if the charge is fractionalized in unit of $1/q$, irrespective of microscopic model or of effective theory. Furthermore, if the quasiparticle is either boson or fermion, it must be at least $q^{2g}$.

4 pages, updated with additional references. No change in the main conclusion

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Cited by in corpus (86)

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• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• Chiral spin liquid phase of the triangular lattice Hubbard model: a density matrix renormalization group study
• A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
• Materials design of Kitaev spin liquids beyond the Jackeli-Khaliullin mechanism
• Generalized modular transformations in 3+1D topologically ordered phases and triple linking invariant of loop braiding
• $Z_2$ spin liquid and chiral antiferromagnetic phase in Hubbard model on the honeycomb lattice: duality between Schwinger-fermion and Schwinger-boson representations
• Spin liquids on a honeycomb lattice: Projective Symmetry Group study of Schwinger fermion mean-field theory
• Counting Rules of Nambu-Goldstone Modes
• Successive Majorana Topological Transitions Driven by a Magnetic Field in the Kitaev Model
• Spurious Long-range Entanglement and Replica Correlation Length
• Fractionally charged topological point defects on the kagome lattice
• Constraints on topological order in Mott Insulators
• Symmetry protected fractional Chern insulators and fractional topological insulators
• Topological degeneracy of non-Abelian states for dummies
• Entanglement signatures of quantum Hall phase transitions
• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Filling-enforced constraint on the quantized Hall conductivity on a periodic lattice
• Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions
• Obtaining topological degenerate ground states by the density matrix renormalization group
• Entanglement Scaling of Fractional Quantum Hall states through Geometric Deformations
• Topologically distinct classes of valence bond solid states with their parent Hamiltonians
• Entanglement between particle partitions in itinerant many-particle states
• Establishing non-Abelian topological order in Gutzwiller projected Chern insulators via Entanglement Entropy and Modular S-matrix
• Ground state degeneracy on torus in a family of ${\mathbb{Z}}_N$ toric code
• Changing topology by topological defects in three-dimensional topologically ordered phases
• Interacting Anyonic Fermions in a Two-Body Color Code Model
• Fractional spin liquid hierarchy for spin S antiferromagnets
• Geometric phases and the magnetization process in quantum antiferromagnets
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• Pretopological fractional excitations in the two-leg flux ladder
• Nature of a topological quantum phase transition in a chiral spin liquid model
• Spin dynamics in the Kitaev model with disorder: Quantum Monte Carlo study of dynamical spin structure factor, magnetic susceptibility, and NMR relaxation rate
• Characterization of topological states on a lattice with Chern number
• Majorana-Magnon Crossover by a Magnetic Field in the Kitaev Model: Continuous-Time Quantum Monte Carlo Study
• Topological Color Codes and Two-Body Quantum Lattice Hamiltonians
• Lieb-Schultz-Mattis type constraints on Fractonic Matter
• General procedure for determining braiding and statistics of anyons using entanglement interferometry
• Nonequilibrium Majorana Dynamics by Quenching a Magnetic Field in Kitaev Spin Liquids
• Solvable Periodic Anderson Model with Infinite-Range Hatsugai-Kohmoto Interaction: Ground-states and beyond
• Non-Symmetry-Breaking Ground State of the S=1 Heisenberg Model on the Kagome lattice
• Explicit monodromy of Moore-Read wave functions on a torus
• Ground state degeneracy of non-Abelian topological phases from coupled wires
• Local Integrals of Motion for Topologically Ordered Many-Body Localized Systems
• Spin quantum Hall effects in a spin-1 topological paramagnet
• Spin-Liquid--to--Spin-Liquid Transition in Kitaev Magnets Driven by Fractionalization
• Variety of order-by-disorder phases in the asymmetric $J_1-J_2$ zigzag ladder: From the delta chain to the $J_1-J_2$ chain
• Topological Discrete Algebra, Ground State Degeneracy, and Quark Confinement in QCD
• Fractional quantum Hall effect in a U(1)xSU(2) gauge field
• Coupled spin-1/2 ladders as microscopic models for non-Abelian chiral spin liquids
• Scaling theory for Mott-Hubbard transitions
• Exotic Non-Abelian Topological Defects in Lattice Fractional Quantum Hall States
• Topological invariants for interacting systems: from twisted boundary condition to center-of-mass momentum
• Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalisation group analysis
• Filling constraints on fermionic topological order in zero magnetic field
• Midgap spectrum of the fermion-vortex system
• Statistics of holes and nature of superfluid phases in Quantum dimer models
• Symmetry protected gapless $Z_2$ spin liquids
• Calculations of Chern number: equivalence of real-space and twisted-boundary-condition formulae
• Fractional Quantum Hall Effect and Featureless Mott Insulators
• Fibonacci anyon excitations of one-dimensional dipolar lattice bosons
• Holographic unitary renormalization group for correlated electrons -- II: insights on fermionic criticality
• Braid Group, Gauge Invariance and Topological Order
• Fractional charges and spin-charge separation in one-dimensional Wigner lattices
• Filling constraints on translation invariant dipole conserving systems
• Coherent information as a mixed-state topological order parameter of fermions
• Quantum Hall effect in momentum space
• Absence of topological degeneracy in the Hubbard model on honeycomb lattice
• Adiabatic Heuristic Principle on a Torus and Generalized Streda Formula
• Lieb-Schultz-Mattis theorem in higher dimensions from approximate magnetic translation symmetry
• $Z_3$ and $(\times Z_3{)}^3$ symmetry protected topological paramagnets
• Robust Topological Degeneracy of Classical Theories
• Fractional quantum Hall states with gapped boundaries in an extreme lattice limit
• Classical and quantum spin liquids
• Disorder-induced topological superconductivity in a spherical quantum-Hall--superconductor hybrid
• Ordering the topological order in the fractional quantum Hall effect
• Topological Aspects of Antiferromagnets
• A primer on Kitaev Model: Basic aspects, material realization, and recent experiments
• Two-dimensional topological paramagnets protected by ${\mathbb{Z}}_3$ symmetry: Properties of the boundary Hamiltonian
• Superconductivity in a system of interacting spinful semions
• Topological Phase Transitions of Interacting Fermions in the Presence of a Commensurate Magnetic Flux
• Partons from stabilizer codes
• Monopole-Enriched Groundstates of Two-Dimensional BCS Models