{ "$schema": "https://qft.org/data/schemas/qft-many-body-comparison-1.0.0.schema.json", "schema_version": "1.0.0", "artifact_id": "qft.artifact.many-body-quantum-matter.quantum-impurities-polarons-kondo-claim-validity-ledger", "table_id": "impurity-claim-test-matrix", "canonical_source": { "route": "/many-body-quantum-matter/quantum-impurities-polarons-kondo/", "heading": "Impurity claim test matrix", "anchor": "impurity-claim-test-matrix" }, "caption": "Impurity regimes, observables, and control tests.", "common_scope": { "markdown": "", "math": [], "links": [] }, "qualifications": { "markdown": "", "math": [], "links": [] }, "columns": [ { "key": "claim_or_regime", "label": "Claim or regime" }, { "key": "fixed_point_or_defining_input", "label": "Fixed point or defining input" }, { "key": "observable", "label": "Observable" }, { "key": "necessary_control", "label": "Necessary control" }, { "key": "decisive_failure_test_or_ceiling", "label": "Decisive failure test or ceiling" } ], "rows": [ { "key": "local-moment-impurity", "row_id": "impurity-claim-test-matrix--local-moment-impurity", "cells": { "claim_or_regime": { "markdown": "Local-moment impurity", "math": [], "links": [] }, "fixed_point_or_defining_input": { "markdown": "Declared local multiplet, bath channels, and positive charge gaps", "math": [], "links": [] }, "observable": { "markdown": "Curie susceptibility and moment-sector probability", "math": [], "links": [] }, "necessary_control": { "markdown": "$T,\\Gamma$ below $E_-$ and $E_+$; symmetry and channel conservation stated", "math": [ { "kind": "inlineMath", "tex": "T,\\Gamma" }, { "kind": "inlineMath", "tex": "E_-" }, { "kind": "inlineMath", "tex": "E_+" } ], "links": [] }, "decisive_failure_test_or_ceiling": { "markdown": "Mixed-valence charge fluctuations are order one or the bath is not the assumed low-energy continuum", "math": [], "links": [] } } }, { "key": "anderson-resonance", "row_id": "impurity-claim-test-matrix--anderson-resonance", "cells": { "claim_or_regime": { "markdown": "Anderson resonance", "math": [], "links": [] }, "fixed_point_or_defining_input": { "markdown": "$\\varepsilon_d$, $U$, and hybridization function $\\Delta^R$", "math": [ { "kind": "inlineMath", "tex": "\\varepsilon_d" }, { "kind": "inlineMath", "tex": "U" }, { "kind": "inlineMath", "tex": "\\Delta^R" } ], "links": [] }, "observable": { "markdown": "Impurity spectral function, occupancy, and charge susceptibility", "math": [], "links": [] }, "necessary_control": { "markdown": "Spectral sum rule, causality, bandwidth, and bath normalization", "math": [], "links": [] }, "decisive_failure_test_or_ceiling": { "markdown": "Claimed feature moves or loses weight under an admissible bath reconstruction", "math": [], "links": [] } } }, { "key": "schrieffer-wolff-kondo-model", "row_id": "impurity-claim-test-matrix--schrieffer-wolff-kondo-model", "cells": { "claim_or_regime": { "markdown": "Schrieffer–Wolff Kondo model", "math": [], "links": [] }, "fixed_point_or_defining_input": { "markdown": "Projection onto a separated moment multiplet", "math": [], "links": [] }, "observable": { "markdown": "Matched exchange $J$, potential scattering $K$, and transformed operators", "math": [ { "kind": "inlineMath", "tex": "J" }, { "kind": "inlineMath", "tex": "K" } ], "links": [] }, "necessary_control": { "markdown": "$\\Gamma/E_\\pm\\ll1$ and cutoff below both charge gaps", "math": [ { "kind": "inlineMath", "tex": "\\Gamma/E_\\pm\\ll1" } ], "links": [] }, "decisive_failure_test_or_ceiling": { "markdown": "Mixed valence or an omitted nearby multiplet invalidates the projection", "math": [], "links": [] } } }, { "key": "perturbative-kondo-scaling", "row_id": "impurity-claim-test-matrix--perturbative-kondo-scaling", "cells": { "claim_or_regime": { "markdown": "Perturbative Kondo scaling", "math": [], "links": [] }, "fixed_point_or_defining_input": { "markdown": "Antiferromagnetic exchange and metallic bath convention", "math": [], "links": [] }, "observable": { "markdown": "Running $j(D)$ and convention-defined $T_K$", "math": [ { "kind": "inlineMath", "tex": "j(D)" }, { "kind": "inlineMath", "tex": "T_K" } ], "links": [] }, "necessary_control": { "markdown": "Density of states, cutoff, and observable definition of $T_K$ fixed", "math": [ { "kind": "inlineMath", "tex": "T_K" } ], "links": [] }, "decisive_failure_test_or_ceiling": { "markdown": "Finite size, temperature, pseudogap, field, or superconducting gap stops the flow first", "math": [], "links": [] } } }, { "key": "exactly-screened-strong-coupling", "row_id": "impurity-claim-test-matrix--exactly-screened-strong-coupling", "cells": { "claim_or_regime": { "markdown": "Exactly screened strong coupling", "math": [], "links": [] }, "fixed_point_or_defining_input": { "markdown": "Conserved metallic channels with $k=2S$", "math": [ { "kind": "inlineMath", "tex": "k=2S" } ], "links": [] }, "observable": { "markdown": "Phase shift, Friedel count, vanishing residual entropy, and analytic local-Fermi-liquid corrections", "math": [], "links": [] }, "necessary_control": { "markdown": "Phase branch, displaced-charge and Luttinger hypotheses, irrelevant-operator regime, and contact geometry", "math": [], "links": [] }, "decisive_failure_test_or_ceiling": { "markdown": "Under- or overscreening or a nonmetallic bath changes the fixed point; asymmetry shifts the phase and can permit a linear spectral term", "math": [], "links": [] } } }, { "key": "overscreened-kondo", "row_id": "impurity-claim-test-matrix--overscreened-kondo", "cells": { "claim_or_regime": { "markdown": "Overscreened Kondo", "math": [], "links": [] }, "fixed_point_or_defining_input": { "markdown": "Channel-symmetric $k>2S$ exchange", "math": [ { "kind": "inlineMath", "tex": "k>2S" } ], "links": [] }, "observable": { "markdown": "Residual entropy and nonanalytic boundary exponents", "math": [], "links": [] }, "necessary_control": { "markdown": "Channel anisotropy, field, spin-assisted interchannel exchange, finite size, and crossover scale controlled", "math": [], "links": [] }, "decisive_failure_test_or_ceiling": { "markdown": "A relevant perturbation drives the system to a Fermi liquid before the claimed window", "math": [], "links": [] } } }, { "key": "nrg-result", "row_id": "impurity-claim-test-matrix--nrg-result", "cells": { "claim_or_regime": { "markdown": "NRG result", "math": [], "links": [] }, "fixed_point_or_defining_input": { "markdown": "Logarithmic discretization and iterated truncated chain", "math": [], "links": [] }, "observable": { "markdown": "Thermodynamics and real-frequency spectra", "math": [], "links": [] }, "necessary_control": { "markdown": "Discretization, kept-state, symmetry, broadening, sum-rule, and exact-limit convergence", "math": [], "links": [] }, "decisive_failure_test_or_ceiling": { "markdown": "Result drifts beyond tolerance under $\\Lambda$, $z$ shift, truncation, or broadening changes", "math": [ { "kind": "inlineMath", "tex": "\\Lambda" }, { "kind": "inlineMath", "tex": "z" } ], "links": [] } } }, { "key": "ct-qmc-result", "row_id": "impurity-claim-test-matrix--ct-qmc-result", "cells": { "claim_or_regime": { "markdown": "CT-QMC result", "math": [], "links": [] }, "fixed_point_or_defining_input": { "markdown": "Specified imaginary-time impurity action", "math": [], "links": [] }, "observable": { "markdown": "Matsubara correlators and thermodynamics", "math": [], "links": [] }, "necessary_control": { "markdown": "Expansion order, sampling, autocorrelation, covariance, tail, stabilization, and sign or phase checks", "math": [], "links": [] }, "decisive_failure_test_or_ceiling": { "markdown": "Analytic continuation is presented as unique or errors fail replica and sum-rule tests", "math": [], "links": [] } } }, { "key": "quantum-dot-spectroscopy", "row_id": "impurity-claim-test-matrix--quantum-dot-spectroscopy", "cells": { "claim_or_regime": { "markdown": "Quantum-dot spectroscopy", "math": [], "links": [] }, "fixed_point_or_defining_input": { "markdown": "Interacting region plus lead and bias model", "math": [], "links": [] }, "observable": { "markdown": "Conductance matrix, temperature and field scaling, and noise", "math": [], "links": [] }, "necessary_control": { "markdown": "Coupling asymmetry, voltage drop, heating, resolution, and nonequilibrium treatment", "math": [], "links": [] }, "decisive_failure_test_or_ceiling": { "markdown": "A dot level, singlet–doublet crossing, or lead artifact fits the same sweeps", "math": [], "links": [] } } }, { "key": "orthogonality-or-x-ray-edge", "row_id": "impurity-claim-test-matrix--orthogonality-or-x-ray-edge", "cells": { "claim_or_regime": { "markdown": "Orthogonality or X-ray edge", "math": [], "links": [] }, "fixed_point_or_defining_input": { "markdown": "Sudden local quench and initial/final phase shifts", "math": [], "links": [] }, "observable": { "markdown": "Overlap exponent and threshold power law", "math": [], "links": [] }, "necessary_control": { "markdown": "Channel count, phase-shift branch, core-hole lifetime, and finite-temperature rounding", "math": [], "links": [] }, "decisive_failure_test_or_ceiling": { "markdown": "Bound-state or excitonic contribution is omitted or no asymptotic scaling window exists", "math": [], "links": [] } } }, { "key": "mobile-polaron", "row_id": "impurity-claim-test-matrix--mobile-polaron", "cells": { "claim_or_regime": { "markdown": "Mobile polaron", "math": [], "links": [] }, "fixed_point_or_defining_input": { "markdown": "Matched impurity–medium scattering and total momentum", "math": [], "links": [] }, "observable": { "markdown": "Pole energy, residue, width, effective mass, molecule and continuum thresholds", "math": [], "links": [] }, "necessary_control": { "markdown": "Density/range parameters, recoil, branch preparation, and spectral sum rule", "math": [], "links": [] }, "decisive_failure_test_or_ceiling": { "markdown": "Peak lacks pole scaling, decays into continuum, or molecule and final-state effects remain viable", "math": [], "links": [] } } }, { "key": "kondo-lattice-competition", "row_id": "impurity-claim-test-matrix--kondo-lattice-competition", "cells": { "claim_or_regime": { "markdown": "Kondo-lattice competition", "math": [], "links": [] }, "fixed_point_or_defining_input": { "markdown": "Local moments, conduction band, $J_K$, and intersite exchange", "math": [ { "kind": "inlineMath", "tex": "J_K" } ], "links": [] }, "observable": { "markdown": "Magnetic ordering, coherence scale, and reconstructed bands", "math": [], "links": [] }, "necessary_control": { "markdown": "Frustration, filling, dimensionality, and self-consistent lattice dynamics", "math": [], "links": [] }, "decisive_failure_test_or_ceiling": { "markdown": "Doniach scale crossing alone is used as a phase boundary or single-impurity $T_K$ is equated with coherence", "math": [ { "kind": "inlineMath", "tex": "T_K" } ], "links": [] } } }, { "key": "heavy-fermi-liquid", "row_id": "impurity-claim-test-matrix--heavy-fermi-liquid", "cells": { "claim_or_regime": { "markdown": "Heavy Fermi liquid", "math": [], "links": [] }, "fixed_point_or_defining_input": { "markdown": "Coherent hybridization and unbroken translation symmetry", "math": [], "links": [] }, "observable": { "markdown": "Low-$T$ Fermi-liquid response and large Fermi-volume consistency", "math": [ { "kind": "inlineMath", "tex": "T" } ], "links": [] }, "necessary_control": { "markdown": "Constraint fluctuations, unit cell, multiband structure, and Luttinger hypotheses", "math": [], "links": [] }, "decisive_failure_test_or_ceiling": { "markdown": "Hybridization mean field fits a band without thermodynamic coherence or correct global counting", "math": [], "links": [] } } }, { "key": "kondo-breakdown-or-local-criticality", "row_id": "impurity-claim-test-matrix--kondo-breakdown-or-local-criticality", "cells": { "claim_or_regime": { "markdown": "Kondo breakdown or local criticality", "math": [], "links": [] }, "fixed_point_or_defining_input": { "markdown": "Critical loss of Kondo coherence in a specified lattice model", "math": [], "links": [] }, "observable": { "markdown": "Joint crossover scale, Fermi-volume-sensitive response, dynamics, and thermodynamics", "math": [], "links": [] }, "necessary_control": { "markdown": "Common tuning variable, width extrapolation, disorder and resolution, held-out predictions", "math": [], "links": [] }, "decisive_failure_test_or_ceiling": { "markdown": "Spin-density-wave, Lifshitz, valence, multiband, or disorder model explains the same combined data", "math": [], "links": [] } } } ], "references": [ { "id": "ref-49811710d684a5bf", "markdown": "Schrieffer, J. R., and Wolff, P. A. (1966). “Relation between the Anderson and Kondo Hamiltonians.” *Physical Review* **149**, 491–492. [doi:10.1103/PhysRev.149.491](https://doi.org/10.1103/PhysRev.149.491).", "urls": [ "https://doi.org/10.1103/PhysRev.149.491" ] } ], "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." }