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    "title": "Finite-size towers connect symmetric quantum ground states to spontaneous symmetry breaking",
    "summary": "Koma and Tasaki related long-range order in symmetric finite-volume quantum states to families of low-energy states and symmetry-breaking infinite-volume ground states. They constructed charge-ladder trial states for local lattice Hamiltonians with a continuous symmetry. Under additional algebraic and discrete-symmetry assumptions, their excitation-energy bound scales as M squared divided by the number of sites, where M labels the charge displacement. Suitable linear combinations yield infinite-volume ground states with nonzero order parameters. A separate result establishes ergodic broken-symmetry limits for a discrete-symmetry setting with an isolated low-energy doublet.",
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        "title": "Symmetry Breaking and Finite Size Effects in Quantum Many-Body Systems (arXivcond-mat/9708132v1;1997postpublicationnotes)",
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            "citation": "Symmetry Breaking and Finite Size Effects in Quantum Many-Body Systems (arXivcond-mat/9708132v1;1997postpublicationnotes)",
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            "citation": "Symmetry Breaking and Finite Size Effects in Quantum Many-Body Systems (arXivcond-mat/9708132v1;1997postpublicationnotes)",
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        "description": "The results are conditional on uniform long-range order, bounded local interactions and the stated symmetry assumptions. The general U(1) theorem controls energy density and has a weaker total-energy bound; the M-squared-over-volume bound requires extra conditions and a specified range of M. Ergodicity of the constructed continuous-symmetry limits remains conjectural in this source. Applications do not prove long-range order for every listed model. The exact1997source adds corrections to the interpretation of particle-number symmetry breaking in its Bose-condensation example; its body is not asserted identical to the 1994 publication.",
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          "citation": "Symmetry Breaking and Finite Size Effects in Quantum Many-Body Systems (arXivcond-mat/9708132v1;1997postpublicationnotes)",
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      "statement": "# Finite-size towers connect symmetric quantum ground states to spontaneous symmetry breaking\n\nKoma and Tasaki related long-range order in symmetric finite-volume quantum states to families of low-energy states and symmetry-breaking infinite-volume ground states. They constructed charge-ladder trial states for local lattice Hamiltonians with a continuous symmetry. Under additional algebraic and discrete-symmetry assumptions, their excitation-energy bound scales as M squared divided by the number of sites, where M labels the charge displacement. Suitable linear combinations yield infinite-volume ground states with nonzero order parameters. A separate result establishes ergodic broken-symmetry limits for a discrete-symmetry setting with an isolated low-energy doublet.\n\n## Scientific scope\n\nThe results are conditional on uniform long-range order, bounded local interactions and the stated symmetry assumptions. The general U(1) theorem controls energy density and has a weaker total-energy bound; the M-squared-over-volume bound requires extra conditions and a specified range of M. Ergodicity of the constructed continuous-symmetry limits remains conjectural in this source. Applications do not prove long-range order for every listed model. The exact1997source adds corrections to the interpretation of particle-number symmetry breaking in its Bose-condensation example; its body is not asserted identical to the 1994 publication.\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\nTohru Koma; Hal Tasaki\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- [Symmetry Breaking and Finite Size Effects in Quantum Many-Body Systems (arXivcond-mat/9708132v1;1997postpublicationnotes)](https://arxiv.org/pdf/cond-mat/9708132v1)\n",
      "summary": "Koma and Tasaki related long-range order in symmetric finite-volume quantum states to families of low-energy states and symmetry-breaking infinite-volume ground states. They constructed charge-ladder trial states for local lattice Hamiltonians with a continuous symmetry. Under additional algebraic and discrete-symmetry assumptions, their excitation-energy bound scales as M squared divided by the number of sites, where M labels the charge displacement. Suitable linear combinations yield infinite-volume ground states with nonzero order parameters. A separate result establishes ergodic broken-symmetry limits for a discrete-symmetry setting with an isolated low-energy doublet.",
      "title": "Finite-size towers connect symmetric quantum ground states to spontaneous symmetry breaking"
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    "title": "Finite-size towers connect symmetric quantum ground states to spontaneous symmetry breaking",
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    "what_changed": "Koma and Tasaki related long-range order in symmetric finite-volume quantum states to families of low-energy states and symmetry-breaking infinite-volume ground states. They constructed charge-ladder trial states for local lattice Hamiltonians with a continuous symmetry. Under additional algebraic and discrete-symmetry assumptions, their excitation-energy bound scales as M squared divided by the number of sites, where M labels the charge displacement. Suitable linear combinations yield infinite-volume ground states with nonzero order parameters. A separate result establishes ergodic broken-symmetry limits for a discrete-symmetry setting with an isolated low-energy doublet.",
    "scope": "Koma and Tasaki related long-range order in symmetric finite-volume quantum states to families of low-energy states and symmetry-breaking infinite-volume ground states. They constructed charge-ladder trial states for local lattice Hamiltonians with a continuous symmetry. Under additional algebraic and discrete-symmetry assumptions, their excitation-energy bound scales as M squared divided by the number of sites, where M labels the charge displacement. Suitable linear combinations yield infinite-volume ground states with nonzero order parameters. A separate result establishes ergodic broken-symmetry limits for a discrete-symmetry setting with an isolated low-energy doublet. The results are conditional on uniform long-range order, bounded local interactions and the stated symmetry assumptions. The general U(1) theorem controls energy density and has a weaker total-energy bound; the M-squared-over-volume bound requires extra conditions and a specified range of M. Ergodicity of the constructed continuous-symmetry limits remains conjectural in this source. Applications do not prove long-range order for every listed model. The exact1997source adds corrections to the interpretation of particle-number symmetry breaking in its Bose-condensation example; its body is not asserted identical to the 1994 publication.",
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