{ "$schema": "https://qft.org/data/schemas/qft-many-body-comparison-1.0.0.schema.json", "schema_version": "1.0.0", "artifact_id": "qft.artifact.many-body-quantum-matter.cold-atoms-synthetic-matter-claim-validity-ledger", "table_id": "cold-atoms-synthetic-matter-claim-test-matrix", "canonical_source": { "route": "/many-body-quantum-matter/cold-atoms-synthetic-matter/", "heading": "Cold-atom and synthetic-matter claim test matrix", "anchor": "cold-atom-and-synthetic-matter-claim-test-matrix" }, "caption": "Calibrated platforms and the conditions on cold-atom and synthetic-matter claims.", "common_scope": { "markdown": "", "math": [], "links": [] }, "qualifications": { "markdown": "", "math": [], "links": [] }, "columns": [ { "key": "platform_or_claim", "label": "Platform or claim" }, { "key": "calibrated_hamiltonian_term", "label": "Calibrated Hamiltonian term" }, { "key": "required_scale_hierarchy", "label": "Required scale hierarchy" }, { "key": "preparation", "label": "Preparation" }, { "key": "observable_and_resolution", "label": "Observable and resolution" }, { "key": "loss_heating_or_discrepancy", "label": "Loss, heating, discrepancy" }, { "key": "evidence_ceiling_through_10_august_2026", "label": "Supported conclusion through 10 August 2026" } ], "rows": [ { "key": "cross-platform-realization", "row_id": "cold-atoms-synthetic-matter-claim-test-matrix--cross-platform-realization", "cells": { "platform_or_claim": { "markdown": "Cross-platform realization", "math": [], "links": [] }, "calibrated_hamiltonian_term": { "markdown": "$H_{\\mathrm{tar}}(\\theta)+\\sum_\\alpha c_\\alpha\\mathcal O_\\alpha$ with covariance", "math": [ { "kind": "inlineMath", "tex": "H_{\\mathrm{tar}}(\\theta)+\\sum_\\alpha c_\\alpha\\mathcal O_\\alpha" } ], "links": [] }, "required_scale_hierarchy": { "markdown": "Retained target scales exceed bounded corrections over declared domain", "math": [], "links": [] }, "preparation": { "markdown": "State, ramp, equilibration, and history fixed", "math": [], "links": [] }, "observable_and_resolution": { "markdown": "Full response matrix with held-out predictions", "math": [], "links": [] }, "loss_heating_or_discrepancy": { "markdown": "Noise, omitted operators, and covariance stress-tested", "math": [], "links": [] }, "evidence_ceiling_through_10_august_2026": { "markdown": "Model compatibility for stated states, sizes, times, and observables", "math": [], "links": [] } } }, { "key": "trapped-continuum-gas", "row_id": "cold-atoms-synthetic-matter-claim-test-matrix--trapped-continuum-gas", "cells": { "platform_or_claim": { "markdown": "Trapped continuum gas", "math": [], "links": [] }, "calibrated_hamiltonian_term": { "markdown": "Kinetic, trap, chemical potential, and matched interaction", "math": [], "links": [] }, "required_scale_hierarchy": { "markdown": "$T/T_F$, $k_Fa$, $k_Fr_e$, $\\hbar\\omega/E_F$, $k_FL$, lifetime", "math": [ { "kind": "inlineMath", "tex": "T/T_F" }, { "kind": "inlineMath", "tex": "k_Fa" }, { "kind": "inlineMath", "tex": "k_Fr_e" }, { "kind": "inlineMath", "tex": "\\hbar\\omega/E_F" }, { "kind": "inlineMath", "tex": "k_FL" } ], "links": [] }, "preparation": { "markdown": "Atom number, entropy, ramps, and holds reproduced", "math": [], "links": [] }, "observable_and_resolution": { "markdown": "Density or correlations after LDA and point-spread map", "math": [], "links": [] }, "loss_heating_or_discrepancy": { "markdown": "Trap gradients, dimensional crossover, loss, heating", "math": [], "links": [] }, "evidence_ceiling_through_10_august_2026": { "markdown": "Local or trap-averaged equation-of-state statement, not automatic phase identity", "math": [], "links": [] } } }, { "key": "feshbach-controlled-gas", "row_id": "cold-atoms-synthetic-matter-claim-test-matrix--feshbach-controlled-gas", "cells": { "platform_or_claim": { "markdown": "Feshbach-controlled gas", "math": [], "links": [] }, "calibrated_hamiltonian_term": { "markdown": "$a(B)$, $r_e$, $R^*$, and confinement-matched coupling", "math": [ { "kind": "inlineMath", "tex": "a(B)" }, { "kind": "inlineMath", "tex": "r_e" }, { "kind": "inlineMath", "tex": "R^*" } ], "links": [] }, "required_scale_hierarchy": { "markdown": "Field covariance small enough; $k_Fr_e$, $k_FR^*$ and loss controlled", "math": [ { "kind": "inlineMath", "tex": "k_Fr_e" }, { "kind": "inlineMath", "tex": "k_FR^*" } ], "links": [] }, "preparation": { "markdown": "Sweep and molecule-association history specified", "math": [], "links": [] }, "observable_and_resolution": { "markdown": "Spectroscopy, binding energy, loss, or many-body response", "math": [], "links": [] }, "loss_heating_or_discrepancy": { "markdown": "Overlapping poles, gradients, optical loss, closed-channel fraction", "math": [], "links": [] }, "evidence_ceiling_through_10_august_2026": { "markdown": "Calibrated scattering window; pole field alone does not prove unitarity", "math": [], "links": [] } } }, { "key": "optical-lattice-hubbard-system", "row_id": "cold-atoms-synthetic-matter-claim-test-matrix--optical-lattice-hubbard-system", "cells": { "platform_or_claim": { "markdown": "Optical-lattice Hubbard system", "math": [], "links": [] }, "calibrated_hamiltonian_term": { "markdown": "Wannier $t_{ij}$, $U$, trap, and leading extended terms", "math": [ { "kind": "inlineMath", "tex": "t_{ij}" }, { "kind": "inlineMath", "tex": "U" } ], "links": [] }, "required_scale_hierarchy": { "markdown": "$t,U,k_BT,\\hbar/t_{\\mathrm{ramp}}\\ll\\Delta_{\\mathrm{band}}$; smaller $J_{\\mathrm ex}$ resolved", "math": [ { "kind": "inlineMath", "tex": "t,U,k_BT,\\hbar/t_{\\mathrm{ramp}}\\ll\\Delta_{\\mathrm{band}}" }, { "kind": "inlineMath", "tex": "J_{\\mathrm ex}" } ], "links": [] }, "preparation": { "markdown": "Loading entropy and spin equilibration tested", "math": [], "links": [] }, "observable_and_resolution": { "markdown": "Site-resolved density and correlations with parity/fidelity map", "math": [], "links": [] }, "loss_heating_or_discrepancy": { "markdown": "Higher bands, $t'$, $V_{ij}$, density-assisted hopping, photon heating", "math": [ { "kind": "inlineMath", "tex": "t'" }, { "kind": "inlineMath", "tex": "V_{ij}" } ], "links": [] }, "evidence_ceiling_through_10_august_2026": { "markdown": "Hubbard realization and observable agreement in benchmarked window", "math": [], "links": [] } } }, { "key": "unitary-fermi-gas", "row_id": "cold-atoms-synthetic-matter-claim-test-matrix--unitary-fermi-gas", "cells": { "platform_or_claim": { "markdown": "Unitary Fermi gas", "math": [], "links": [] }, "calibrated_hamiltonian_term": { "markdown": "Zero-range broad-resonance fixed point plus range corrections", "math": [], "links": [] }, "required_scale_hierarchy": { "markdown": "$\\lvert k_Fa\\rvert^{-1}$, $\\lvert k_Fr_e\\rvert$, trap and imbalance small as claimed", "math": [ { "kind": "inlineMath", "tex": "\\lvert k_Fa\\rvert^{-1}" }, { "kind": "inlineMath", "tex": "\\lvert k_Fr_e\\rvert" } ], "links": [] }, "preparation": { "markdown": "Equilibrium and thermometry established", "math": [], "links": [] }, "observable_and_resolution": { "markdown": "Dimensionless EOS, contact, spectral or superfluid observable with convention", "math": [], "links": [] }, "loss_heating_or_discrepancy": { "markdown": "Range, trap, final-state response, analytic continuation", "math": [], "links": [] }, "evidence_ceiling_through_10_august_2026": { "markdown": "Universal scaling relations; numerical benchmarks retain method uncertainty", "math": [], "links": [] } } }, { "key": "dipolar-or-molecular-gas", "row_id": "cold-atoms-synthetic-matter-claim-test-matrix--dipolar-or-molecular-gas", "cells": { "platform_or_claim": { "markdown": "Dipolar or molecular gas", "math": [], "links": [] }, "calibrated_hamiltonian_term": { "markdown": "Contact plus anisotropic dressed interaction and internal channels", "math": [], "links": [] }, "required_scale_hierarchy": { "markdown": "Diluteness, confinement, shielding gap, thermalization and lifetime", "math": [], "links": [] }, "preparation": { "markdown": "Polarization, dressing, evaporation, and internal-state purity fixed", "math": [], "links": [] }, "observable_and_resolution": { "markdown": "Momentum spectrum, coherence, modulation, expansion, or loss", "math": [], "links": [] }, "loss_heating_or_discrepancy": { "markdown": "Short-range collision model, LHY boundary, two-/three-body loss", "math": [], "links": [] }, "evidence_ceiling_through_10_august_2026": { "markdown": "Roton, condensate, droplet, or coherence evidence for stated protocol", "math": [], "links": [] } } }, { "key": "synthetic-gauge-or-spin-orbit-gas", "row_id": "cold-atoms-synthetic-matter-claim-test-matrix--synthetic-gauge-or-spin-orbit-gas", "cells": { "platform_or_claim": { "markdown": "Synthetic gauge or spin–orbit gas", "math": [], "links": [] }, "calibrated_hamiltonian_term": { "markdown": "Berry connection, scalar potential, SOC or Floquet Hamiltonian", "math": [], "links": [] }, "required_scale_hierarchy": { "markdown": "Dressed gap exceeds Doppler, interaction, temperature, ramp; drive avoids resonances", "math": [], "links": [] }, "preparation": { "markdown": "Laser phases, detuning, polarization, timing controlled", "math": [], "links": [] }, "observable_and_resolution": { "markdown": "Band geometry, Wilson-loop or dynamics with micromotion map", "math": [], "links": [] }, "loss_heating_or_discrepancy": { "markdown": "Spontaneous emission, nonadiabaticity, Floquet heating, projection", "math": [], "links": [] }, "evidence_ceiling_through_10_august_2026": { "markdown": "Calibrated gauge dynamics; interacting topological phase requires separate tests", "math": [], "links": [] } } }, { "key": "moire-flat-band-device", "row_id": "cold-atoms-synthetic-matter-claim-test-matrix--moire-flat-band-device", "cells": { "platform_or_claim": { "markdown": "Moiré flat-band device", "math": [], "links": [] }, "calibrated_hamiltonian_term": { "markdown": "Continuum/downfolded bands plus screened form-factor interaction", "math": [], "links": [] }, "required_scale_hierarchy": { "markdown": "$W$, isolation gaps, $E_C$, temperature, disorder, remote bands quantified", "math": [ { "kind": "inlineMath", "tex": "W" }, { "kind": "inlineMath", "tex": "E_C" } ], "links": [] }, "preparation": { "markdown": "Density, displacement field, twist/strain map, history fixed", "math": [], "links": [] }, "observable_and_resolution": { "markdown": "Compressibility, spectroscopy, transport, thermodynamics with contacts", "math": [], "links": [] }, "loss_heating_or_discrepancy": { "markdown": "Relaxation, screening, flavor polarization, domains, inhomogeneity", "math": [], "links": [] }, "evidence_ceiling_through_10_august_2026": { "markdown": "Device-specific band or phase evidence; filling alone has no phase content", "math": [], "links": [] } } }, { "key": "certified-analog-simulation", "row_id": "cold-atoms-synthetic-matter-claim-test-matrix--certified-analog-simulation", "cells": { "platform_or_claim": { "markdown": "Certified analog simulation", "math": [], "links": [] }, "calibrated_hamiltonian_term": { "markdown": "Target, discrepancy operators, preparation and measurement channels", "math": [], "links": [] }, "required_scale_hierarchy": { "markdown": "Exact limits and benchmark regime overlap the claimed domain", "math": [], "links": [] }, "preparation": { "markdown": "Calibration data separated from validation data", "math": [], "links": [] }, "observable_and_resolution": { "markdown": "Held-out observable vector with full covariance", "math": [], "links": [] }, "loss_heating_or_discrepancy": { "markdown": "Adversarial faults, solver discrepancy, extrapolation failure", "math": [], "links": [] }, "evidence_ceiling_through_10_august_2026": { "markdown": "Bounded model-realization certificate, never proof beyond tested domain", "math": [], "links": [] } } } ], "references": [ { "id": "ref-7dd577c6922e2d7f", "markdown": "Bloch, I., Dalibard, J., and Nascimbène, S. (2012). “Quantum simulations with ultracold quantum gases.” *Nature Physics* **8**, 267–276. [doi:10.1038/nphys2259](https://doi.org/10.1038/nphys2259).", "urls": [ "https://doi.org/10.1038/nphys2259" ] } ], "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." }