Many-Body Results

Many-body result cards make model class and limiting assumptions visible. A finite lattice, thermodynamic limit, short-range interaction, power-law tail, exact symmetry, or spectral gap can change both the theorem and its conclusion. The cards here are compact lookup layers; their linked canonical owners retain proofs, derivations, examples, and extension boundaries.

Helpful background. Lieb–Robinson Bounds is the full owner for the locality result. Use it whenever the metric, interaction norm, support prefactor, thermodynamic-limit argument, or velocity convention matters.

Locality card

• Lieb–Robinson Bound states a volume-uniform commutator estimate for bounded short-range quantum lattice dynamics and gives its minimum hypothesis and limitation checklist.

Other many-body cards appear in the sidebar. Their route names are not evidence that their statements, prerequisites, or canonical owners have passed review.

Assumption discipline

Before applying a many-body result, identify:

• the metric space and support notion;
• finite volume versus thermodynamic limit;
• finite-range, exponential, or algebraic interaction decay;
• bounded versus unbounded observables and interactions;
• bosonic tensor-product locality versus fermionic graded locality;
• state-independent operator bounds versus state-dependent correlation or transport statements;
• every additional gap, symmetry, temperature, dimensionality, or initial-state assumption used by the desired consequence.

For the current card, the safest workflow is to start with the exact $F$-function statement, derive the needed tolerance contour, and only then translate it into the phrase “effective light cone.”

Card-owner contract

• The card owns compact lookup and no proof.
• The rigorous owner owns the precise decay norm, constants, proof architecture, infinite-volume consequence, variants, and exercises.
• A consequence such as exponential clustering or phase stability must name its additional hypotheses and theorem.
• A velocity extracted from data must not be identified with a convenient Lieb–Robinson upper bound without a separate argument.

References

• E. H. Lieb and D. W. Robinson, “The Finite Group Velocity of Quantum Spin Systems,” Communications in Mathematical Physics 28, 251–257, 1972, doi:10.1007/BF01645779.
• B. Nachtergaele and R. Sims, “Lieb–Robinson Bounds in Quantum Many-Body Physics,” Contemporary Mathematics 529, 141–176, 2010, doi:10.1090/conm/529/10429.
• B. Nachtergaele, R. Sims, and A. Young, “Quasi-Locality Bounds for Quantum Lattice Systems. Part I. Lieb–Robinson Bounds, Quasi-Local Maps, and Spectral Flow Automorphisms,” Journal of Mathematical Physics 60, 061101, 2019, doi:10.1063/1.5095769.