{ "$schema": "https://qft.org/data/schemas/qft-many-body-comparison-1.0.0.schema.json", "schema_version": "1.0.0", "artifact_id": "qft.artifact.many-body-quantum-matter.fractional-quantum-hall-anyons-claim-validity-ledger", "table_id": "fractional-hall-claim-validity-table", "canonical_source": { "route": "/many-body-quantum-matter/fractional-quantum-hall-anyons/", "heading": "Claim-validity table", "anchor": "claim-validity-table" }, "caption": "Candidate fractional Hall orders and tests of their topological predictions.", "common_scope": { "markdown": "", "math": [], "links": [] }, "qualifications": { "markdown": "", "math": [], "links": [] }, "columns": [ { "key": "proposed_order", "label": "Proposed order" }, { "key": "filling_and_shift", "label": "Filling and shift" }, { "key": "topological_input", "label": "Topological input" }, { "key": "quasiparticles", "label": "Quasiparticles" }, { "key": "edge_prediction", "label": "Edge prediction" }, { "key": "closed_manifold_and_entanglement_test", "label": "Closed-manifold and entanglement test" }, { "key": "experimental_discriminator", "label": "Experimental discriminator" }, { "key": "principal_ambiguity", "label": "Principal ambiguity" } ], "rows": [ { "key": "laughlin-1-m", "row_id": "fractional-hall-claim-validity-table--laughlin-1-m", "cells": { "proposed_order": { "markdown": "Laughlin $1/m$", "math": [ { "kind": "inlineMath", "tex": "1/m" } ], "links": [] }, "filling_and_shift": { "markdown": "$\\nu=1/m$, sphere shift $m$", "math": [ { "kind": "inlineMath", "tex": "\\nu=1/m" }, { "kind": "inlineMath", "tex": "m" } ], "links": [] }, "topological_input": { "markdown": "$K=(m)$, $t=(1)$", "math": [ { "kind": "inlineMath", "tex": "K=(m)" }, { "kind": "inlineMath", "tex": "t=(1)" } ], "links": [] }, "quasiparticles": { "markdown": "Minimal charge $e/m$, exchange $\\pi/m$", "math": [ { "kind": "inlineMath", "tex": "e/m" }, { "kind": "inlineMath", "tex": "\\pi/m" } ], "links": [] }, "edge_prediction": { "markdown": "One chiral boson, $c_-=1$", "math": [ { "kind": "inlineMath", "tex": "c_-=1" } ], "links": [] }, "closed_manifold_and_entanglement_test": { "markdown": "$m^g$ genus-$g$ sectors; $\\gamma=\\tfrac12\\ln m$", "math": [ { "kind": "inlineMath", "tex": "m^g" }, { "kind": "inlineMath", "tex": "g" }, { "kind": "inlineMath", "tex": "\\gamma=\\tfrac12\\ln m" } ], "links": [] }, "experimental_discriminator": { "markdown": "Hall plateau plus charge and statistical-phase tests", "math": [], "links": [] }, "principal_ambiguity": { "markdown": "Edge reconstruction, Coulomb-dominated interference, or finite-size charge-density order", "math": [], "links": [] } } }, { "key": "jain-abelian-state", "row_id": "fractional-hall-claim-validity-table--jain-abelian-state", "cells": { "proposed_order": { "markdown": "Jain Abelian state", "math": [], "links": [] }, "filling_and_shift": { "markdown": "$\\nu=p/(2sp\\pm1)$; shift sequence-dependent", "math": [ { "kind": "inlineMath", "tex": "\\nu=p/(2sp\\pm1)" } ], "links": [] }, "topological_input": { "markdown": "Multicomponent $K,t$ or projected composite-fermion state", "math": [ { "kind": "inlineMath", "tex": "K,t" } ], "links": [] }, "quasiparticles": { "markdown": "Charges and braiding from $K^{-1}$", "math": [ { "kind": "inlineMath", "tex": "K^{-1}" } ], "links": [] }, "edge_prediction": { "markdown": "Several modes; upstream content depends on signature and equilibration", "math": [], "links": [] }, "closed_manifold_and_entanglement_test": { "markdown": "Expected torus manifold and counting after momentum folding", "math": [], "links": [] }, "experimental_discriminator": { "markdown": "Charge, thermal, and interface equilibration compared jointly", "math": [], "links": [] }, "principal_ambiguity": { "markdown": "Spin/valley polarization, Landau-level mixing, and alternative hierarchy state", "math": [], "links": [] } } }, { "key": "candidate-non-abelian-state", "row_id": "fractional-hall-claim-validity-table--candidate-non-abelian-state", "cells": { "proposed_order": { "markdown": "Candidate non-Abelian state", "math": [], "links": [] }, "filling_and_shift": { "markdown": "Filling and shift candidate-specific", "math": [], "links": [] }, "topological_input": { "markdown": "Fusion category or CFT data plus charge sector", "math": [], "links": [] }, "quasiparticles": { "markdown": "Quantum dimension greater than one; matrix braid action", "math": [], "links": [] }, "edge_prediction": { "markdown": "Charged plus neutral sectors; candidate-specific $c_-$", "math": [ { "kind": "inlineMath", "tex": "c_-" } ], "links": [] }, "closed_manifold_and_entanglement_test": { "markdown": "Fusion-space growth, modular data, entanglement counting, size convergence", "math": [], "links": [] }, "experimental_discriminator": { "markdown": "Fusion-channel-sensitive interferometry and equilibrated thermal response", "math": [], "links": [] }, "principal_ambiguity": { "markdown": "Abelian competitor, edge nonequilibration, disorder, or insufficient size", "math": [], "links": [] } } }, { "key": "fractional-chern-insulator", "row_id": "fractional-hall-claim-validity-table--fractional-chern-insulator", "cells": { "proposed_order": { "markdown": "Fractional Chern insulator", "math": [], "links": [] }, "filling_and_shift": { "markdown": "Fractional lattice-band filling; no universal shift on a torus", "math": [], "links": [] }, "topological_input": { "markdown": "Many-body Chern response and topological data", "math": [], "links": [] }, "quasiparticles": { "markdown": "Lattice analogues of continuum anyons", "math": [], "links": [] }, "edge_prediction": { "markdown": "Depends on boundary and lattice symmetry", "math": [], "links": [] }, "closed_manifold_and_entanglement_test": { "markdown": "Spectral flow, manifold counting, entanglement, absence of density order", "math": [], "links": [] }, "experimental_discriminator": { "markdown": "Zero-field fractional Hall response with independent incompressibility and magnetism tests", "math": [], "links": [] }, "principal_ambiguity": { "markdown": "Competing charge/magnetic order, inhomogeneity, band mixing, or device-dependent phase diagram", "math": [], "links": [] } } }, { "key": "interferometric-anyon-claim", "row_id": "fractional-hall-claim-validity-table--interferometric-anyon-claim", "cells": { "proposed_order": { "markdown": "Interferometric anyon claim", "math": [], "links": [] }, "filling_and_shift": { "markdown": "Filling and localized quasiparticle number fixed", "math": [], "links": [] }, "topological_input": { "markdown": "Predicted Aharonov–Bohm plus statistical phase", "math": [], "links": [] }, "quasiparticles": { "markdown": "Charge and braid phase or fusion channel stated", "math": [], "links": [] }, "edge_prediction": { "markdown": "Coherent edge path with calibrated area and velocity", "math": [], "links": [] }, "closed_manifold_and_entanglement_test": { "markdown": "Not sufficient alone", "math": [], "links": [] }, "experimental_discriminator": { "markdown": "Phase slips/periods tied to controlled quasiparticle addition and reproduced across regimes", "math": [], "links": [] }, "principal_ambiguity": { "markdown": "Coulomb charging, area breathing, telegraph traps, neutral-mode dephasing, and selection", "math": [], "links": [] } } }, { "key": "entanglement-identification", "row_id": "fractional-hall-claim-validity-table--entanglement-identification", "cells": { "proposed_order": { "markdown": "Entanglement identification", "math": [], "links": [] }, "filling_and_shift": { "markdown": "Geometry, cut, and conserved sectors stated", "math": [], "links": [] }, "topological_input": { "markdown": "Candidate total quantum dimension and edge counting", "math": [], "links": [] }, "quasiparticles": { "markdown": "Sector-dependent quantum dimensions if resolved", "math": [], "links": [] }, "edge_prediction": { "markdown": "Low-lying counting may mirror an edge CFT", "math": [], "links": [] }, "closed_manifold_and_entanglement_test": { "markdown": "Multi-size extrapolation of entropy and entanglement gap", "math": [], "links": [] }, "experimental_discriminator": { "markdown": "Indirect; must agree with response or quasiparticle tests", "math": [], "links": [] }, "principal_ambiguity": { "markdown": "Nonuniversal area term, cut dependence, aliasing, and small-system mimicry", "math": [], "links": [] } } } ], "references": [ { "id": "ref-df3bb5fe6cb0c40a", "markdown": "Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, and Sankar Das Sarma, “Non-Abelian Anyons and Topological Quantum Computation,” *Reviews of Modern Physics* **80** (2008) 1083–1159, [doi:10.1103/RevModPhys.80.1083](https://doi.org/10.1103/RevModPhys.80.1083).", "urls": [ "https://doi.org/10.1103/RevModPhys.80.1083" ] } ], "reference_scope": "The reference catalog reproduces the canonical chapter bibliography. Cell links are associated with references only when their resolved URL matches; uncited chapter references are not asserted as claim-specific support." }