Pith Number

pith:BRAU6HZG

pith:2026:BRAU6HZGPJ4A5VJST3E42NY5WS

not attested not anchored not stored refs resolved

Local Topological Quantum Order and Spectral Gap Stability for the AKLT Models on the Hexagonal and Lieb Lattices

Amanda Young, Bruno Nachtergaele, Thomas Jackson

Ground states of AKLT models on hexagonal and Lieb lattices satisfy local topological quantum order with exponential boundary decay.

arxiv:2605.12184 v2 · 2026-05-12 · math-ph · cond-mat.str-el · math.MP · quant-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BRAU6HZGPJ4A5VJST3E42NY5WS}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The ground states of the AKLT models on the hexagonal lattice and the Lieb lattice satisfy the local topological quantum order (LTQO) condition, with finite-volume ground-state expectations approximating the infinite-volume state at a uniform exponential rate in the distance to the boundary; as a corollary the spectral gap is stable under general small perturbations of sufficient decay.

C2weakest assumption

The polymer representation of the ground state derived by Kennedy, Lieb and Tasaki (1988) admits the necessary modifications to establish the strong form of ground-state indistinguishability required for LTQO on these specific lattices (see abstract and the detailed analysis section referenced therein).

C3one line summary

Proves LTQO for AKLT models on hexagonal and Lieb lattices by modifying the 1988 polymer representation to obtain uniform exponential decay of boundary effects.

References

45 extracted · 45 resolved · 2 Pith anchors

[1] H. Abdul-Rahman, M. Lemm, A. Lucia, B. Nachtergaele, and A. Young. A class of two-dimensional AKLT models with a gap. In A. Young H. Abdul-Rahman, R. Sims, editor,Analytic Trends in Mathematical Physi 2020

[2] I. Affleck, T. Kennedy, E.H. Lieb, and H. Tasaki. Rigorous results on valence-bond ground states in antiferro- magnets.Phys. Rev. Lett., 59:799, 1987 1987

[3] I. Affleck, T. Kennedy, E.H. Lieb, and H. Tasaki. Valence bond ground states in isotropic quantum antiferro- magnets.Comm. Math. Phys., 115(3):477–528, 1988 1988

[4] D.P. Arovas, A. Auerbach, and F.D.M. Haldane. Extended heisenberg models of antiferromagnetism: Analogies to the fractional quantum hall effect.Phys. Rev. Lett., 60:531–534, 1988 1988

[5] S. Bachmann, E. Hamza, B. Nachtergaele, and A. Young. Product Vacua and Boundary State models ind dimensions.J. Stat. Phys., 160:636–658, 2015 2015

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:43.957353Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c414f1f267a780ed5329ec9cd371db4b5677d748f41834addec046cc340b1a8

Aliases

arxiv: 2605.12184 · arxiv_version: 2605.12184v2 · doi: 10.48550/arxiv.2605.12184 · pith_short_12: BRAU6HZGPJ4A · pith_short_16: BRAU6HZGPJ4A5VJS · pith_short_8: BRAU6HZG

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BRAU6HZGPJ4A5VJST3E42NY5WS \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0c414f1f267a780ed5329ec9cd371db4b5677d748f41834addec046cc340b1a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7684bfb7c9ea098015868fb67de391bdbd6de819a6fa7e5156ee1324a2b86bfc",
    "cross_cats_sorted": [
      "cond-mat.str-el",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-05-12T14:27:09Z",
    "title_canon_sha256": "3024a3a2f5a0c7fc581e0192563a4887b2dc20766c65db7185c54d565be5da87"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12184",
    "kind": "arxiv",
    "version": 2
  }
}