Model-to-Volume Cross-Link Index

A recurring model can legitimately appear in several places, but each appearance must do a different job. A model dossier fixes the reproducible mathematical object. A teaching article derives its physics. A reference card locates it quickly. A benchmark tests an implementation. An application volume owns a material, atomic, device, or field-theory realization.

This index assigns those roles so that “another Hubbard page” or “another Ising page” does not silently become a second canonical home.

Canonical Scope

This page is the canonical home for cross-volume routing decisions for many-body models. It records:

• the live dossier for every model in the Model Encyclopedia;
• the topical page that owns derivations and physical interpretation;
• compact Reference cards and Hamiltonian entries where they exist;
• stable numerical benchmark contracts;
• application-volume ownership and the current live gateway;
• controlled limits that connect one dossier to another;
• criteria for deciding whether a proposed page is a model, method, application, benchmark, or duplicate.

The Model Encyclopedia remains the canonical comparison of model families, conventions, solvability claims, and observables. Common Many-Body Hamiltonians and Common Spin Hamiltonians remain the compact formula references. This index routes among those layers; it does not rederive their content.

When a reader starts from a material observable rather than a named model, Choosing a Model for Quantum Matter owns the inverse selection audit. This index begins after a model family is named and routes its dossier, teaching, reference, benchmark, and application owners.

For a named spin model applied to a material, Magnetism and Spin Systems is the application gateway: it separates moment, exchange, ordered-phase, excitation, itinerant, response, and texture questions without replacing the dossier or teaching owner.

Routing Layers

Layer	Owns	Does not own
model dossier	Hilbert space, Hamiltonian convention, geometry, symmetries, limits, solution status, observables	every derivation or application
teaching article	derivation, mechanism, phase structure, approximations, physical interpretation	short cross-site lookup
formula sheet or Hamiltonian entry	one compact convention-aware expression	a complete model specification
Reference model card	concise locator and aliases	a second teaching article
benchmark contract	finite input, expected output, tolerances, validation	the general model family
application volume	material, atomic, optical, information-processing, or device realization	abstract model formalism already owned here
QFT or frontier bridge	continuum limit, renormalization, large-$N$ structure, open research status	elementary many-body definitions

Status language

• Live means the route exists and is linked below.
• Planned means an explanation is unfinished. Authored scaffolds are available, but a roadmap or substantive gateway may provide a more useful starting point.
• No separate card means the dossier is the current compact locator. It is not a request to create a duplicate automatically.
• Generic card means one Reference card covers several geometries, such as both a Hubbard dimer and chain.

Choose the Route by Question

Reader question	First destination
What exactly is meant by this model name?	model dossier
Which sign, normalization, boundary, or ensemble convention is used?	dossier, then formula sheet
How is the spectrum, mapping, or phase structure derived?	topical teaching article
Is there a one-screen formula or alias lookup?	Reference card or Hamiltonian entry
How do I test my code?	benchmark contract and reproducible-notebook index
How is the model realized with atoms or light?	Atomic, Molecular, and Optical Physics for the ownership map, then the specialized application treatment
What does the model explain in a material?	Choosing a Model for Quantum Matter, then the narrow material application owner
Which algorithm should I use?	Computational Many-Body QM or Computational Quantum Mechanics
What is the continuum, RG, or large-$N$ interpretation?	QFT bridge or frontier page

Live Model Routing Matrix

The dossier column is always the canonical model specification. Other columns route to distinct responsibilities.

Gases and collective chains

Model dossier	Teaching or derivation home	Compact lookup and validation	Application destination
Ideal Bose Gas	Ideal Bose Gas owns thermodynamics and condensation	Bose Gas card; Bose Gas Formula Sheet; MB-B006	Atomic, Molecular, and Optical Physics owns traps and realization; use the AMO roadmap for a guided route into the specialized treatments
Ideal Fermi Gas	Ideal Fermi Gas owns Fermi surfaces and low-temperature thermodynamics	Fermi Gas card; Fermi Gas Formula Sheet; MB-B007	Quantum gases use the AMO roadmap; electron-gas applications begin with Choosing a Model for Quantum Matter
Harmonic Chain	Phonons as Many-Body Excitations owns the normal-mode and phonon derivation	no separate global card; the dossier contains its matrix benchmark	Material force constants, optical branches, scattering, and lifetimes begin with Choosing a Model for Quantum Matter
Lieb–Liniger Model Preview	Low-Dimensional Quantum Gases and Nonrelativistic Field Theory own the broader context	no separate global card; Exact Solutions Preview classifies the Bethe-ansatz method	Quasi-one-dimensional cold-atom realization belongs to Atomic, Molecular, and Optical Physics; current AMO roadmap
Tonks–Girardeau Gas Preview	Low-Dimensional Quantum Gases owns the gas regime; Luttinger Liquid Preview owns the infrared language	no separate global card; the dossier owns the finite-ring Bose–Fermi benchmark	Confinement and experimental realization belong to Atomic, Molecular, and Optical Physics; current AMO roadmap

Spin and quadratic lattice families

Model dossier	Teaching or derivation home	Compact lookup and validation	Application destination
Spin-1/2 Chain	Lattice Models Overview owns the shared local-spin framework	Common Spin Hamiltonians; Symmetry Sectors	Magnetic materials go to Quantum Matter; spin simulators go to Atomic, Molecular, and Optical Physics or Quantum Information
Transverse-Field Ising Model	Transverse-Field Ising Model owns Jordan–Wigner, Bogoliubov, critical, and entanglement derivations	Ising Chain card; Ising Hamiltonian; MB-B001; MB-B009	Magnetic realization belongs to Quantum Matter; simulator and information applications use the quantum-information roadmap
Heisenberg Chain	Heisenberg Model owns exchange physics, dimensions, order, and chain limits	Heisenberg Chain card; Heisenberg Hamiltonian; MB-B002	Magnetic materials and spin waves begin with Choosing a Model for Quantum Matter
XXZ Chain	XXZ Spin Chain owns anisotropy, phases, Bethe equations, and Luttinger behavior	Common Spin Hamiltonians; no separate XXZ card	Magnetic realizations begin with Choosing a Model for Quantum Matter; cold-atom realizations use the AMO roadmap
Tight-Binding Chain	Tight-Binding Model owns Fourier diagonalization, bands, flux, and localization boundaries	Tight-Binding Chain card; Common Many-Body Hamiltonians	Bloch bands, Wannier functions, materials, and topological band models begin with Choosing a Model for Quantum Matter

Interacting lattice models

Model dossier	Teaching or derivation home	Compact lookup and validation	Application destination
Hubbard Dimer	Exact Hubbard Dimer Spectrum owns the teaching derivation	generic Hubbard card; Hubbard Hamiltonian; MB-B003	The dimer is primarily a benchmark and few-site laboratory; do not create a material-specific duplicate
Hubbard Chain	Hubbard Model owns generic formalism, strong coupling, observables, and methods	generic Hubbard card; Hubbard Hamiltonian; MB-B004	Mott physics and correlated materials belong to Quantum Matter; optical-lattice realization belongs to Atomic, Molecular, and Optical Physics
Bose–Hubbard Dimer	Bose–Hubbard Model owns the generic lattice-boson formalism; the dossier owns the exact fixed-$N$ dimer	generic Bose–Hubbard card; MB-B005	Double-well preparation and measurement belong to Atomic, Molecular, and Optical Physics; current AMO roadmap
Bose–Hubbard Chain	Bose–Hubbard Model owns the generic model and mean-field boundary; the dossier owns one-dimensional limits and benchmarks	generic Bose–Hubbard card; Finite-Size Scaling in Numerics	Optical lattices and calibration belong to Atomic, Molecular, and Optical Physics; quantum critical phenomenology cross-links to Quantum Matter

Pairing, impurities, and frontier models

Model dossier	Teaching or derivation home	Compact lookup and validation	Application destination
Reduced BCS Model	the dossier owns Richardson’s exact finite-level solution; BCS Mean-Field Theory owns the bulk symmetry-breaking saddle	BCS Model card; Common Many-Body Hamiltonians; MB-B008 tests the separate mean-field equation	Superconducting phenomenology, materials, Meissner response, and devices belong to Quantum Matter
Kondo Model	Kondo Model Preview owns screening, scaling, and method comparison	no separate global card; Effective Hamiltonians owns the Anderson-to-Kondo reduction	Impurity phenomenology and heavy fermions belong to Quantum Matter; full RG belongs beyond the preview, with the QFT bridge roadmap as current route
Anderson Impurity Model	Anderson Impurity Model Preview owns spectra, regimes, transport, and DMFT context	no separate global card; Effective Hamiltonians owns the low-energy projection	Quantum dots, magnetic impurities, and correlated-material embeddings belong to their application volumes
SYK Model Preview	Large-N Methods Preview owns saddle logic; Scrambling and OTOCs Preview owns chaos diagnostics	no separate global card; the dossier owns the finite-$N$ benchmark and convention ledger	Many-body chaos and holographic interpretation belong to Research Frontiers and QFT bridges; current QFT bridge roadmap

Reference Coverage

The global Reference is intentionally sparser than the Model Encyclopedia.

Coverage type	Live entries	Routing rule
generic many-body cards	Bose gas, Fermi gas, Hubbard, Bose–Hubbard, BCS	one card can point to several geometries and dossiers
spin-model cards	Ising chain, Heisenberg chain	use cards for global lookup; use dossiers for convention and benchmark detail
condensed-matter card	tight-binding chain	Choosing a Model for Quantum Matter owns the live material-to-model selection audit; the narrow application owner develops the material physics
Hamiltonian entries	Hubbard, Ising chain, Heisenberg chain	formula entry is not a model dossier
dossier-only models	harmonic chain, spin-$1/2$ umbrella, XXZ, Kondo, Anderson, Lieb–Liniger, Tonks–Girardeau, SYK	create a card only when cross-site discovery needs it; never copy the dossier body

A missing card is not a missing model page. The live dossier remains the stable destination until a genuinely shorter cross-site locator is useful.

Cross-Volume Ownership

Application volumes mature at different rates. Use the live gateway in the last column rather than a placeholder article URL.

Destination	Owns	Does not duplicate	Current live route
Quantum Matter	bands in solids, phonons in materials, magnetism, Mott phenomenology, superconductivity, Kondo effect, heavy fermions	abstract Hubbard, spin-chain, pairing, or impurity model definitions	Choosing a Model for Quantum Matter
Atomic, Molecular, and Optical Physics	trap construction, Feshbach tuning, optical lattices, loading, imaging, cold-atom realizations	ideal-gas derivations or generic Hubbard-family formalism	AMO Physics Roadmap
Quantum Information and Computation	simulator encodings, circuits, control protocols, information-processing use	generic Ising or Heisenberg derivations	Quantum Information Roadmap
Computational Quantum Mechanics	reusable algorithms, data formats, production workflows, cross-volume benchmark suites	physical interpretation already owned by the model volume	Computational Quantum Mechanics Roadmap
Research Frontiers	unresolved model regimes, quantum simulation frontiers, strange metals, SYK-like chaos	standard results already mature in a dossier	Researcher Refresher and model-specific live previews
QFT bridge	continuum fields, renormalization, effective actions, large-$N$ methods, holographic interpretation	elementary Hilbert-space and Hamiltonian definitions	Bridge to QFT Roadmap

Formalism versus phenomenology

The abstract Hubbard Hamiltonian and its controlled limits belong in Many-Body and Quantum Statistical Mechanics. A page about a cuprate, transition-metal oxide, or material-specific Mott regime belongs in Quantum Matter and should link back to the generic formalism.

Likewise, the reduced BCS Hamiltonian and many-body mean-field method are formal objects. Meissner response, critical fields, vortices, Josephson devices, and material phenomenology belong in Quantum Matter.

Model versus realization

The Bose–Hubbard model is defined independently of how it is engineered. Wannier reduction, lattice-depth calibration, confinement, Feshbach control, imaging, and loss mechanisms belong to Atomic, Molecular, and Optical Physics. The model page can derive the effective parameters at overview depth, but it does not own the full experimental apparatus.

Model versus method

Exact diagonalization, DMRG, quantum Monte Carlo, numerical renormalization group, and dynamical mean-field theory are methods. A model dossier states which methods are controlled or customary; the method page owns algorithmic derivation and convergence. Benchmark contracts connect the two without merging them.

Controlled-Limit Handoffs

A relation between models is a cross-link only after the approximation, projected Hilbert space, and observable range are stated.

Tight binding to Hubbard families

The spinful Hubbard model reduces to a quadratic tight-binding problem at

$$U=0.$$

The Bose–Hubbard model likewise becomes quadratic at zero onsite interaction, subject to bosonic stability and chemical-potential conditions. This limit links to Tight-Binding Model; it does not make the interacting dossier redundant.

Hubbard to Heisenberg

For repulsive Hubbard physics near one particle per site and

$$U\gg |t|,$$

the low-energy no-double-occupancy sector has antiferromagnetic exchange

$$J = \frac{4t^2}{U}.$$

Effective Hamiltonians in Many-Body Systems owns the projection, additive density term, and higher-order correction audit. Hubbard Model and Heisenberg Model remain distinct canonical pages because their Hilbert spaces and regimes differ.

Anderson to Kondo

The local-moment regime of the Anderson impurity model admits a Schrieffer–Wolff projection when impurity charge excitations are well separated from the low-energy sector. The resulting exchange model omits the projected charge dynamics. The canonical handoff is:

1. Anderson Impurity Model dossier;
2. Anderson Impurity Model Preview;
3. Anderson-to-Kondo effective Hamiltonian;
4. Kondo Model dossier.

The Kondo page should not reproduce impurity charge spectra, and the Anderson page should not claim the projected spin model is exact outside its scale-separated regime.

Lieb–Liniger to Tonks–Girardeau

For density $n$ and contact coupling $g_{mathrm{1D}}$, a standard dimensionless interaction is

$$\gamma := \frac{m g_{\mathrm{1D}}} {\hbar^2 n}.$$

The impenetrable limit is

$$\gamma\to+\infty.$$

The Lieb–Liniger dossier owns finite coupling and Bethe equations. The Tonks–Girardeau dossier owns the limiting Bose–Fermi map and its observable-specific caveats. Spectra and density observables can map simply while off-diagonal bosonic correlations retain nonlocal strings.

Bose–Hubbard to hard-core spin models

Projecting the repulsive Bose–Hubbard model to

$$n_i\in\{0,1\}$$

maps its hopping to an $XY$ exchange in a field. Large but finite $U$ still permits virtual double occupation and generates corrections. Bose–Hubbard Model owns the projection; XXZ Spin Chain owns the broader anisotropic spin family.

Transverse-field Ising to quadratic fermions

The standard nearest-neighbor chain without a longitudinal field maps to a quadratic fermion problem after Jordan–Wigner transformation. Periodic spin boundaries become parity-dependent fermion boundaries. Jordan–Wigner Transformation owns that bookkeeping. Adding generic longitudinal fields or interactions destroys the same free-fermion solution.

Harmonic chain to phonon field

The long-wavelength harmonic chain gives an elastic scalar field after the lattice spacing is taken small with mass density and stiffness held fixed. The continuum field loses Brillouin-zone and lattice-cutoff information. The dossier owns the reproducible chain; Phonons as Many-Body Excitations owns the collective-mode interpretation.

Reduced BCS exact solution and mean field

The finite reduced Hamiltonian conserves number and admits Richardson roots. The thermodynamic BCS saddle breaks $U(1)$ at mean-field level and uses gap and number equations. In an appropriate continuum limit, the root distribution reproduces the mean-field equations, but an unprojected BCS state is not an exact generic finite-system eigenstate. Keep the exact dossier and mean-field article separate.

When a Variant Deserves a Page

Create a separate dossier only when the variant changes a durable part of the model contract.

Strong reasons to split

• The Hilbert space changes, as between soft-core and strictly hard-core bosons.
• Geometry creates a reusable exact problem, as for Hubbard and Bose–Hubbard dimers.
• Boundary or parity structure changes the solution in a persistent way.
• The variant has an independent exact solution, benchmark, or canonical observable set.
• The literature treats the object as a stable model family rather than one parameter point.

Weak reasons to split

• A coupling is assigned one numerical value.
• The chain length changes only for a finite-size calculation.
• Open boundaries replace periodic boundaries without a broader conceptual change.
• A new solver is applied to the same physical object.
• One material, atom, or device realizes the generic model.
• A compact Hamiltonian has already been written elsewhere.

Weak reasons usually call for a subsection, benchmark, method page, or application page rather than another model dossier.

Canonical-Home Decision Procedure

Before creating a model-related page, answer these questions in order:

1. Is the mathematical object already specified by a live dossier? If yes, link it.
2. Is the proposed content a derivation or physical mechanism? Put it in the topical teaching chapter.
3. Is it a material or experimental realization? Route it to the application volume.
4. Is it an algorithm or convergence study? Route it to a computational method or benchmark.
5. Is it a one-screen formula or alias? Add or extend a reference card.
6. Does a controlled limit change the Hilbert space or effective degrees of freedom? Cross-link both models and put the derivation in an effective-method page.
7. Is the destination still an empty scaffold? Label it Planned and also link a substantive explanation or useful roadmap. A scaffold cannot replace a substantive canonical owner.

If none of these questions establishes a distinct responsibility, the proposed page is probably a duplicate.

Alias and Naming Index

Name or alias	Route and caution
transverse-field Ising chain, TFIM	Transverse-Field Ising dossier; state the Pauli-versus-spin normalization
XXX chain	Heisenberg Chain at isotropic exchange; field and sign conventions still matter
XXZ chain	XXZ Chain; define the anisotropy $\Delta$ and exchange sign
Fermi–Hubbard model	generic Hubbard Model unless a multicomponent or unusual-statistics variant is intended
Bose–Hubbard model, BH model	Bose–Hubbard Model; avoid the bare acronym in mixed contexts
single-impurity Anderson model, SIAM	Anderson Impurity Model dossier; distinguish it from Anderson localization
$s$–$d$ exchange model	commonly the Kondo Model; specify one- versus multichannel and impurity representation
reduced BCS, constant-pairing, Richardson model	Reduced BCS Model; do not conflate its exact finite solution with mean-field BCS
delta-function Bose gas	Lieb–Liniger Model Preview; state the coupling and boundary convention
impenetrable Bose gas	Tonks–Girardeau Gas Preview; the fermion map is observable dependent
Sachdev–Ye–Kitaev model, SYK	SYK Model Preview; state Majorana or complex fermions, interaction order, variance, and disorder averaging

Worked Routing Cases

Hubbard model in a cuprate

• The abstract Hamiltonian and controlled limits link to the Hubbard teaching article and Hubbard Chain dossier when one-dimensional structure matters.
• Material parameters, charge-transfer physics, orbitals, spectroscopy, and comparison with a cuprate belong to Quantum Matter.
• A small-cluster solver validation links to MB-B003 or MB-B004.

One page should not own all three responsibilities.

Bose–Hubbard optical-lattice experiment

• The effective Hamiltonian and phase-structure conventions link to Bose–Hubbard Model.
• A two-well exact calculation links to the Bose–Hubbard Dimer.
• Lattice beams, Wannier calibration, loading, microscopy, and losses belong to Atomic, Molecular, and Optical Physics.
• General critical scaling links to Quantum Phase Transitions rather than being rederived in an experimental page.

BCS superconductivity

After naming the pairing model, enter Superfluidity and Superconductivity to route the material phase or response claim; this index retains model-layer ownership.

• Exact finite-level pairing uses the Reduced BCS Model.
• The bulk anomalous saddle and gap equation use BCS Mean-Field Theory.
• London Theory owns local Meissner electrodynamics; critical fields, tunneling phenomenology, vortices, and Josephson devices also belong to Quantum Matter.
• A one-screen locator uses the BCS Model card.

Calling all four pages “the BCS model” hides their distinct state spaces and observables.

Anderson impurity and Kondo screening

• Begin with the charge-fluctuating Anderson dossier.
• Use the effective-Hamiltonian derivation only in the local-moment regime.
• Continue to the Kondo dossier for the projected exchange model.
• Put resistivity minima, heavy-fermion materials, and Kondo lattices in Quantum Matter; put full field-theoretic RG in the QFT destination.

SYK and black-hole language

• The random Hamiltonian, normalization, disorder average, large-$N$ saddle, and finite-$N$ benchmark stay in the SYK dossier.
• Operator growth and chaos diagnostics use Scrambling and OTOCs Preview.
• Schwarzian theory, holographic interpretation, and gravity claims belong to QFT or Research Frontiers and must retain their approximation and evidence status.

Maintenance Contract

Every new or substantially revised dossier should expose four outgoing links when the destinations exist:

1. its topical teaching home;
2. its compact card or formula sheet;
3. its numerical benchmark or method page;
4. its application or QFT destination.

The reciprocal pages should link back only when the dossier improves navigation. A dense teaching article does not need links to every model variant, but it should link to the canonical dossiers it explicitly uses.

Link stability

• Link to semantic routes, not sidebar order numbers.
• Prefer a live section anchor only when the section is the canonical handoff.
• Do not publish links to planned but nonexistent pages.
• When a future destination goes live, replace the roadmap fallback and leave the model dossier unchanged unless its ownership boundary also changes.
• A redirect can preserve old inbound URLs, but it does not justify maintaining two canonical bodies.

Metadata consistency

The canonical_home field should identify the page that owns the current article’s content, not the broadest related topic. A compact lookup page can point to a deeper canonical article; a unique routing index can own itself. related metadata should mirror important reader paths but cannot replace visible contextual links.

Common Mistakes

Treating the shortest page as canonical

A Reference card is intentionally brief. Canonical ownership follows responsibility, not word count.

Treating a Hamiltonian formula as a complete model

Statistics, Hilbert space, geometry, boundary conditions, ensemble, and observables are part of the model contract.

Creating one page per solver

ED, DMRG, Monte Carlo, NRG, and mean field are methods applied to a model. Put solver-specific derivations and convergence in method pages and link one model dossier.

Turning every finite size into a model

A dimer can deserve a dossier because it is a reusable exact benchmark. A seven-site and nine-site chain normally do not deserve separate canonical pages.

Mixing exact and effective models

Hubbard-to-Heisenberg, Anderson-to-Kondo, and Lieb–Liniger-to-Tonks relations have domains of validity. An arrow is not an identity of complete Hilbert spaces and observables.

Sending formalism to an application volume

Material or cold-atom pages should import the abstract model, not redefine its algebra and conventions independently.

Publishing dead future links

Planned ownership remains distinct from current canonical ownership until the destination supplies a substantive explanation. Use a substantive gateway or useful roadmap for the current treatment.

Assuming a missing card means missing content

The Model Encyclopedia dossier is already a stable page. A second short card is warranted only by cross-site discovery needs.

Exercises

Exercise 1: Route a Mott-material article

A proposed article contains the Hubbard Hamiltonian, a strong-coupling derivation, material-specific orbital parameters for a nickelate, an exact-diagonalization convergence study, and comparison with spectroscopy. Assign each part to its canonical layer.

Solution

• The Hamiltonian convention links to the Hubbard dossier, compact card, or Hamiltonian entry.
• The strong-coupling derivation belongs to Effective Hamiltonians in Many-Body Systems.
• Nickelate orbitals, parameters, and spectroscopy belong to Quantum Matter.
• Solver convergence belongs to a computational method or benchmark page.
• The material article links these pieces and owns the physical synthesis; it should not copy their derivations.

Exercise 2: Decide whether a new dossier is needed

An author proposes separate model pages for open Hubbard chains of lengths $L=6$, $8$, and $10$, all at the same filling and couplings, because each was used in a finite-size study. Should the pages be created?

Solution

No. The system sizes form one finite-size sequence of the same model. Record the geometry and sizes in a benchmark, notebook, or numerical study and link the Hubbard Chain dossier. Separate pages would duplicate the Hamiltonian, symmetries, and observables without establishing new canonical responsibilities.

Exercise 3: Route an optical-lattice claim

An experiment realizes a one-dimensional Bose–Hubbard chain and reports a commensurate transition. Which pages own the effective model, apparatus, transition framework, and finite-size inference?

Solution

• Bose–Hubbard Model owns the effective Hamiltonian and its generic phases.
• The Bose–Hubbard Chain dossier owns one-dimensional conventions and controlled limits.
• Atomic, Molecular, and Optical Physics owns the optical-lattice construction and measurement protocol.
• Quantum Phase Transitions and Universality own the general critical classification.
• Finite-Size Scaling in Numerics owns the inference protocol.

Exercise 4: Audit an Anderson-to-Kondo shortcut

A draft replaces an Anderson impurity model by a Kondo exchange Hamiltonian for every impurity level and hybridization, then uses the Kondo model to predict charge-transfer peaks. Identify the routing error.

Solution

The Schrieffer–Wolff handoff requires a local-moment regime with charge excitations separated from the low-energy sector. The Kondo model has projected those charge fluctuations out and therefore cannot own charge-transfer peaks. The draft must keep the Anderson Impurity Model for charge spectra, state the projection assumptions, and use the Kondo Model only for the resulting low-energy spin exchange.

References

1. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, “Theory of Superconductivity,” Physical Review 108, 1175–1204 (1957), doi:10.1103/PhysRev.108.1175.
2. M. Girardeau, “Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension,” Journal of Mathematical Physics 1, 516–523 (1960), doi:10.1063/1.1703687.
3. P. W. Anderson, “Localized Magnetic States in Metals,” Physical Review 124, 41–53 (1961), doi:10.1103/PhysRev.124.41.
4. E. Lieb, T. Schultz, and D. Mattis, “Two Soluble Models of an Antiferromagnetic Chain,” Annals of Physics 16, 407–466 (1961), doi:10.1016/0003-4916(61)90115-4.
5. J. Hubbard, “Electron Correlations in Narrow Energy Bands,” Proceedings of the Royal Society A 276, 238–257 (1963), doi:10.1098/rspa.1963.0204.
6. E. H. Lieb and W. Liniger, “Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State,” Physical Review 130, 1605–1616 (1963), doi:10.1103/PhysRev.130.1605.
7. R. W. Richardson, “A Restricted Class of Exact Eigenstates of the Pairing-Force Hamiltonian,” Physics Letters 3, 277–279 (1963), doi:10.1016/0031-9163(63)90259-2.
8. J. Kondo, “Resistance Minimum in Dilute Magnetic Alloys,” Progress of Theoretical Physics 32, 37–49 (1964), doi:10.1143/PTP.32.37.
9. J. R. Schrieffer and P. A. Wolff, “Relation between the Anderson and Kondo Hamiltonians,” Physical Review 149, 491–492 (1966), doi:10.1103/PhysRev.149.491.
10. E. H. Lieb and F. Y. Wu, “Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension,” Physical Review Letters 20, 1445–1448 (1968), doi:10.1103/PhysRevLett.20.1445.
11. P. Pfeuty, “The One-Dimensional Ising Model with a Transverse Field,” Annals of Physics 57, 79–90 (1970), doi:10.1016/0003-4916(70)90270-8.
12. S. Sachdev and J. Ye, “Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet,” Physical Review Letters 70, 3339–3342 (1993), doi:10.1103/PhysRevLett.70.3339.

Cross-Links

• Model Encyclopedia
• Choosing a Model for Quantum Matter
• Common Many-Body Hamiltonians
• Common Spin Hamiltonians
• Benchmark Problems
• Reproducible Notebooks
• What Belongs Here vs Quantum Matter vs QFT.org
• AMO Physics Roadmap
• Computational Quantum Mechanics Roadmap
• Bridge to QFT Roadmap