{"paper":{"title":"Lieb-Schultz-Mattis theorem from gauge constraints","license":"http://creativecommons.org/licenses/by/4.0/","headline":"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.","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.str-el","authors_text":"Bhandaru Phani Parasar","submitted_at":"2026-05-13T14:40:56Z","abstract_excerpt":"We construct a $\\mathbb{Z}_2 \\times \\mathbb{Z}_2$ gauge theory coupled to matter on a one-dimensional chain, aiming to study the ground-state physics in the Gauss law subspace. 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. Any point in the parameter space must realize a "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"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.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"cf7246aa1fc5bbe21081370d26a3ada4541f6e84e1b9be89d405b9e44e26d606"},"source":{"id":"2605.13606","kind":"arxiv","version":1},"verdict":{"id":"3be2e40d-b063-4310-926b-d962f2a1c1c1","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T17:50:44.122896Z","strongest_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.","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"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."},"references":{"count":58,"sample":[{"doi":"","year":1961,"title":"E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Annals of Physics16, 407 (1961)","work_id":"92d69014-d24c-4358-9610-2726afec6cbd","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1986,"title":"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)","work_id":"e5454d4b-dd16-496c-8ff4-f489a0df24d5","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1984,"title":"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)","work_id":"f4d492da-d0c0-4734-b0ed-f12bebe2db13","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2000,"title":"Oshikawa, Commensurability, excitation gap, and topology in quantum many-particle systems on a peri- odic lattice, Phys","work_id":"749832fd-b47d-4226-96a6-bad94f3f1619","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2004,"title":"M. B. Hastings, Lieb-schultz-mattis in higher dimensions, Phys. Rev. B69, 104431 (2004)","work_id":"48548aaa-756b-4ccc-a6e1-9806a9997c3f","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":58,"snapshot_sha256":"e3044cc9427d3c9d04c923fe04d223feee4bf2f9a24bcac409c548ae81f87059","internal_anchors":1},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}