TFIM — model index
The 1D transverse-field Ising model — the canonical exactly-solvable quantum phase transition, Jordan-Wigner dual to free fermions and critical at $h = J$.
\[H = -J\sum_i \sigma^z_i \sigma^z_{i+1} - h\sum_i \sigma^x_i\]
Generated by docs/atlas/generate.jl — a pure VIEW over the *_registry.jl claims + the static test/INVENTORY.jsonl AST scan. No test is executed and no src is run; test/INVENTORY.jsonl is regenerated in-place (idempotently) from that static scan; fetch/@register untouched. Assurance labels are PROVISIONAL: residuals / confidence are not shown yet (RES not wired). Badges reflect the committed test AST, not the latest CI run — a hub can read green while its @test is red between regenerations. @sweep = a graceful regime-resolution gap, not card omission.
All (Quantity, BC) hubs src claims for TFIM. Cells link to the per-hub card; — = not yet implemented at that BC. The shape of the matrix is the gap visualisation: empty cells are where physics could be added next.
Convention
| Field | Value |
|---|---|
| Hamiltonian | Pauli σ (this file) |
| Observable | Spin S = σ/2 (QAtlas-wide spin convention; see docs/src/conventions.md) |
Coverage
| Level | Count |
|---|---|
| 🟣 universality-corroborated | 0 |
| 🟢 corroborated-at-p | 36 |
| 🔵 coherent | 8 |
| ⚪ cited-only | 0 |
| 🟠 uncorroborated-but-feasible | 17 |
| total claimed hubs | 61 |
Methods (from @register, derived): analytic, bdg, cft, closed_form, delegation, pfaffian
Quantity × BC matrix
| Quantity | OBC | PBC | Infinite |
|---|---|---|---|
CentralCharge | — | — | 🟢 hub |
ConformalTower | 🟠 hub | 🟠 hub | — |
CorrelationLength | — | — | 🟢 hub |
CriticalExponents | — | — | 🟠 hub |
Energy | 🟢 hub | 🟢 hub | 🟢 hub |
EnergyLocal | 🟠 hub | — | — |
FidelitySusceptibility | 🟢 hub | — | 🟢 hub |
FreeEnergy | 🟢 hub | 🟢 hub | 🟢 hub |
GGEValue | — | — | 🔵 hub |
LiebRobinsonBound | — | — | 🟠 hub |
LiebRobinsonVelocity | — | — | 🟠 hub |
LoschmidtEcho | 🟢 hub | — | 🟢 hub |
MagnetizationX | 🟢 hub | 🟢 hub | 🟢 hub |
MagnetizationXLocal | 🟠 hub | — | 🔵 hub |
MagnetizationY | 🟢 hub | — | — |
MagnetizationZ | — | — | 🟢 hub |
MagnetizationZLocal | 🟠 hub | — | — |
MassGap | 🟢 hub | 🟠 hub | 🟢 hub |
NMRRelaxationExponent | — | — | 🟠 hub |
NMRSpinRelaxationRate | 🟠 hub | — | 🟠 hub |
RenyiEntropy | 🟢 hub | — | 🟠 hub |
SpecificHeat | 🟢 hub | 🟢 hub | 🔵 hub |
SpontaneousMagnetization | — | — | 🟢 hub |
SusceptibilityXX | 🟢 hub | 🟢 hub | 🟠 hub |
SusceptibilityYY | 🟢 hub | — | — |
SusceptibilityZZ | 🟢 hub | — | 🟠 hub |
ThermalEntropy | 🟢 hub | 🟢 hub | 🔵 hub |
UniversalityClass | — | — | 🟠 hub |
VonNeumannEntropy | 🟢 hub | — | 🟠 hub |
XXCorrelation | 🟢 hub | — | 🟢 hub |
XXStructureFactor | 🟢 hub | — | 🔵 hub |
YYCorrelation | 🟢 hub | — | — |
YYStructureFactor | 🟢 hub | — | 🔵 hub |
ZZCorrelation | 🟢 hub | — | — |
ZZStructureFactor | 🔵 hub | — | 🔵 hub |
Derivation notes
Matched by filename substring (no annotation; substrate-derived):
ad-thermodynamics-from-z.mdcalabrese-cardy-obc-vs-pbc.mde8-mass-spectrum-derivation.mdising-cft-magnetic-perturbation.mdising-cft-primary-operators.mdising-scaling-relations.mdjw-tfim-bdg.mdkramers-wannier-duality.mdtfim-entanglement-peschel.mdtfim-gge.mdtfim-loschmidt.mdtfim-sigma-x-quench.mdtransfer-matrix-symmetric-split.mdxx-quench.mdyang-magnetization-toeplitz.md
References
Papers cited by this model's @register cards. The full numbered list is on the Reference List.
- [30]
- E. Barouch, B. M. McCoy and M. Dresden. Statistical Mechanics of the XY Model. I. Physical Review A 2, 1075–1092 (1970).
- [28]
- A. Belavin, A. Polyakov and A. Zamolodchikov. Infinite conformal symmetry in two-dimensional quantum field theory. Nuclear Physics B 241, 333–380 (1984).
- [31]
- H. W. Blöte, J. L. Cardy and M. P. Nightingale. Conformal invariance, the central charge, and universal finite-size amplitudes at criticality. Physical Review Letters 56, 742–745 (1986).
- [32]
- P. Calabrese and J. Cardy. Entanglement entropy and quantum field theory. Journal of Statistical Mechanics: Theory and Experiment 2004, P06002 (2004).
- [33]
- P. Calabrese and J. Cardy. Entanglement entropy and conformal field theory (2009), arXiv:0905.4013.
- [34]
- P. Calabrese, F. H. Essler and M. Fagotti. Quantum quench in the transverse field Ising chain: I. Time evolution of order parameter correlators. Journal of Statistical Mechanics: Theory and Experiment 2012, P07016 (2012).
- [35]
- J. L. Cardy. Operator content of two-dimensional conformally invariant theories. Nuclear Physics B 270, 186–204 (1986).
- [36]
- B. Damski. Fidelity susceptibility of the quantum Ising model in a transverse field: The exact solution. Physical Review E 87 (2013).
- [37]
- S.-J. Gu. Fidelity approach to quantum phase transitions. International Journal of Modern Physics B 24, 4371–4458 (2010).
- [38]
- M. B. Hastings and T. Koma. Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006).
- [39]
- M. Heyl, A. Polkovnikov and S. Kehrein. Dynamical Quantum Phase Transitions in the Transverse-Field Ising Model. Physical Review Letters 110 (2013).
- [40]
- M. Heyl. Dynamical quantum phase transitions: a review. Reports on Progress in Physics 81, 054001 (2018).
- [41]
- E. H. Lieb and D. W. Robinson. The finite group velocity of quantum spin systems. Communications in Mathematical Physics 28, 251–257 (1972).
- [9]
- E. Lieb, T. Schultz and D. Mattis. Two soluble models of an antiferromagnetic chain. Annals of Physics 16, 407–466 (1961).
- [42]
- L. Onsager. Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition. Physical Review 65, 117–149 (1944).
- [43]
- I. Peschel. Calculation of reduced density matrices from correlation functions. Journal of Physics A: Mathematical and General 36, L205–L208 (2003).
- [11]
- P. Pfeuty. The one-dimensional Ising model with a transverse field. Annals of Physics 57, 79–90 (1970).
- [44]
- M. Rigol, V. Dunjko, V. Yurovsky and M. Olshanii. Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons. Physical Review Letters 98 (2007).
- [45]
- S. Sachdev. Theory of finite-temperature crossovers near quantum critical points close to, or above, their upper-critical dimension. Physical Review B 55, 142–163 (1997).
- [46]
- S. Sachdev. Quantum Phase Transitions (2011).