AWhat 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.
Scientific 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.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. 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.
Contributors
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