[challenge]: Certified exclusion in the kagome spin-liquid controversy

Released by

Jie Wang (AMSS, Chinese Academy of Sciences) & Jin-Guo Liu (Hong Kong University of Science and Technology (Guangzhou))

Contact email

cacate0129@gmail.com

Method

Other

Challenge issue

Difficulty: ★★★ (rated by Jie Wang)

Background

The ground state of the spin-1/2 kagome Heisenberg antiferromagnet is a two-decade condensed-matter controversy — gapped Z2 vs. gapless U(1) Dirac spin liquid — where variational methods disagree with each other. Certified lower-bound technology has recently reached frustrated 3D magnets (pyrochlore Anderson-type bounds, arXiv:2601.07800) and property certification at scale (arXiv:2310.05844, arXiv:2604.01555).

Research objective

Push certified bounds on the kagome energy density — Anderson-type cluster hierarchies with certified subadditivity, full wallpaper-group + SU(2) symmetry reduction, 2D transfer of RG compression (arXiv:2212.03014), spectral-gap certificates for the gapped scenario — until they exclude one competing ground-state class, or at least beat every prior rigorous bound.

Verification plan

• Success gate: a certified energy-density interval that provably excludes the published variational energy of at least one candidate class (numeric comparison against fixed literature values), or a certified gap bound incompatible with the gapless scenario over a stated window.
• Hope signal: a certified window strictly tighter than the best prior rigorous kagome bound — a record with a proof, publishable regardless of exclusion.
• Pivot signal: 2D relaxations plateau far above variational energies at every reachable level — quantify and publish the obstruction analysis.

Why this may lead to research output

A certified bound takes sides in a famous debate with a proof rather than another ansatz — a first-of-its-kind contribution at the optimization/condensed-matter interface.

References

1. Kránitz et al., Rigorous Anderson-type lower bounds for the pyrochlore Heisenberg antiferromagnet, arXiv:2601.07800.
2. Wang et al., Certifying ground-state properties of many-body systems, arXiv:2310.05844 (PRX).
3. Wang et al., Scalable ground-state certification of quantum spin systems, arXiv:2604.01555.

The issue names no repository files, tests, or entry points; begin by inspecting the Python repository structure and existing challenge implementations. Define the certified kagome bound and verification gate from the issue, then document whether an exclusion, tighter bound, or quantified plateau result is achieved.