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    "title": "Non-symmorphic crystal symmetries obstruct trivial insulators at selected integer fillings",
    "summary": "Parameswaran, Turner, Arovas and Vishwanath extended filling constraints on insulating states to non-symmorphic crystals, whose symmetries combine point operations with fractional translations. A flux-threading argument shows how a conserved charge can change screw or glide quantum numbers even when the filling per cell is an integer. This rules out a unique symmetry-preserving trivial insulator at selected integer fillings, sharpening the usual fractional-filling obstruction. The paper connects the constraint to band connectivity and gives spin and boson applications.",
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        "description": "The argument assumes conserved U(1) charge, exact crystal symmetry and the stated insulating flux-response framework. Its electronic treatment neglects spin-orbit coupling and counts filling per spin component. It provides necessary conditions for trivial insulators, not a construction or a diagnosis of the phase of every listed material. A gapped symmetric state at an obstructed filling is interpreted as topologically ordered; symmetry breaking and gaplessness are alternatives. The simplified flux path inherits energy-control arguments rather than proving a complete new uniform bound in this paper.",
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      "statement": "# Non-symmorphic crystal symmetries obstruct trivial insulators at selected integer fillings\n\nParameswaran, Turner, Arovas and Vishwanath extended filling constraints on insulating states to non-symmorphic crystals, whose symmetries combine point operations with fractional translations. A flux-threading argument shows how a conserved charge can change screw or glide quantum numbers even when the filling per cell is an integer. This rules out a unique symmetry-preserving trivial insulator at selected integer fillings, sharpening the usual fractional-filling obstruction. The paper connects the constraint to band connectivity and gives spin and boson applications.\n\n## Scientific scope\n\nThe argument assumes conserved U(1) charge, exact crystal symmetry and the stated insulating flux-response framework. Its electronic treatment neglects spin-orbit coupling and counts filling per spin component. It provides necessary conditions for trivial insulators, not a construction or a diagnosis of the phase of every listed material. A gapped symmetric state at an obstructed filling is interpreted as topologically ordered; symmetry breaking and gaplessness are alternatives. The simplified flux path inherits energy-control arguments rather than proving a complete new uniform bound in this paper.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nSiddharth A. Parameswaran; Ari M. Turner; Daniel P. Arovas; Ashvin Vishwanath\n\nThese are the listed authors of the cited contribution sources. Paper authorship does not quantify individual effort. An incomplete list is explicitly marked; same names are not automatically merged.\n\n\n\n## Original sources\n\n- [Topological Order and Absence of Band Insulators at Integer Filling in Non-Symmorphic Crystals (arXiv1212.0557v2)](https://arxiv.org/pdf/1212.0557v2)\n",
      "summary": "Parameswaran, Turner, Arovas and Vishwanath extended filling constraints on insulating states to non-symmorphic crystals, whose symmetries combine point operations with fractional translations. A flux-threading argument shows how a conserved charge can change screw or glide quantum numbers even when the filling per cell is an integer. This rules out a unique symmetry-preserving trivial insulator at selected integer fillings, sharpening the usual fractional-filling obstruction. The paper connects the constraint to band connectivity and gives spin and boson applications.",
      "title": "Non-symmorphic crystal symmetries obstruct trivial insulators at selected integer fillings"
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    "scope": "Parameswaran, Turner, Arovas and Vishwanath extended filling constraints on insulating states to non-symmorphic crystals, whose symmetries combine point operations with fractional translations. A flux-threading argument shows how a conserved charge can change screw or glide quantum numbers even when the filling per cell is an integer. This rules out a unique symmetry-preserving trivial insulator at selected integer fillings, sharpening the usual fractional-filling obstruction. The paper connects the constraint to band connectivity and gives spin and boson applications. The argument assumes conserved U(1) charge, exact crystal symmetry and the stated insulating flux-response framework. Its electronic treatment neglects spin-orbit coupling and counts filling per spin component. It provides necessary conditions for trivial insulators, not a construction or a diagnosis of the phase of every listed material. A gapped symmetric state at an obstructed filling is interpreted as topologically ordered; symmetry breaking and gaplessness are alternatives. The simplified flux path inherits energy-control arguments rather than proving a complete new uniform bound in this paper.",
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