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pith:35WJKJJ5

pith:2026:35WJKJJ5WKHYJ2IVAKOGRCL3MZ

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Lieb-Schultz-Mattis theorem from gauge constraints

Bhandaru Phani Parasar

Imposing the Gauss law in a Z2 gauge theory on a one-dimensional chain produces a U(1) symmetry that commutes with translations but anticommutes with reflection, forbidding trivial gapped ground states.

arxiv:2605.13606 v1 · 2026-05-13 · cond-mat.str-el · cond-mat.stat-mech

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Claims

C1strongest claim

We show that the theory in the Gauss law subspace has a U(1) symmetry whose generator commutes with lattice translations, but anticommutes with the lattice reflection operator. This leads to a Lieb-Schultz-Mattis (LSM) theorem that always rules out a trivial gapped ground state in the Gauss law subspace, if the hamiltonian is invariant under translations and reflection.

C2weakest assumption

The Hamiltonian remains invariant under both lattice translations and reflection while the system is strictly confined to the Gauss law subspace; if either invariance or the strict subspace projection fails, the U(1) symmetry and resulting LSM theorem do not hold.

C3one line summary

A Z2xZ2 gauge theory on a 1D chain yields an LSM theorem via a U(1) symmetry generated by the Gauss law constraint, ruling out trivial gapped states under translation and reflection symmetry.

References

58 extracted · 58 resolved · 1 Pith anchors

[1] E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Annals of Physics16, 407 (1961) 1961

[2] I. Affleck and E. H. Lieb, A proof of part of haldane’s con- jecture on spin chains, Letters in Mathematical Physics 12, 57 (1986) 1986

[3] M. Oshikawa, M. Yamanaka, and I. Affleck, Magneti- zation plateaus in spin chains: “haldane gap” for half- integer spins, Phys. Rev. Lett.78, 1984 (1997) 1984

[4] Oshikawa, Commensurability, excitation gap, and topology in quantum many-particle systems on a peri- odic lattice, Phys 2000

[5] M. B. Hastings, Lieb-schultz-mattis in higher dimensions, Phys. Rev. B69, 104431 (2004) 2004

Receipt and verification

First computed	2026-05-18T02:44:18.111031Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df6c95253db28f84e915029c68897b665f21b2a7c1e2855a32661e44c4cf5973

Aliases

arxiv: 2605.13606 · arxiv_version: 2605.13606v1 · doi: 10.48550/arxiv.2605.13606 · pith_short_12: 35WJKJJ5WKHY · pith_short_16: 35WJKJJ5WKHYJ2IV · pith_short_8: 35WJKJJ5

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/35WJKJJ5WKHYJ2IVAKOGRCL3MZ \
  | 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: df6c95253db28f84e915029c68897b665f21b2a7c1e2855a32661e44c4cf5973

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ca6c3a7703e9521a833b985845e29d65bed9e0e794313549fd5e742b22d1dd8",
    "cross_cats_sorted": [
      "cond-mat.stat-mech"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.str-el",
    "submitted_at": "2026-05-13T14:40:56Z",
    "title_canon_sha256": "1a473a1136bf1c254871c422be3211eed54d5b582759e3578fc961242b8774cc"
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  "source": {
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    "kind": "arxiv",
    "version": 1
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}