Observations on the Bethe ansatz solutions of the spin-1/2 isotropic anti-ferromagnetic Heisenberg chain: the chiral string conjecture
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Bibliographic record
Abstract
Abstract Calculations of low lying excited states in even length L → ∞ chains begun in 2019 J. Phys. Commun. 3 025007 in the total spin S = 0 sector are here extended to S > 0. Bethe string configurations that were observed to transition from their definition at small L to different ‘apparent’ configurations at large L are now understood to be a manifestation of the approximate chiral symmetry that develops with increasing chain length. It is conjectured that when chiral symmetry is built into the configuration definitions a complete explicit labelling of all low lying excited states by strings is obtained. The structure is of the form of a product of Bethe strings defining left and right chiral states of spin s L and s R and a central complex ‘string’ necessary to bind <?CDATA ${\vec{{\rm{s}}}}_{L}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mi mathvariant="normal">s</mml:mi> <mml:mo>⃗</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> </mml:msub> </mml:math> and <?CDATA ${\vec{{\rm{s}}}}_{R}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mi mathvariant="normal">s</mml:mi> <mml:mo>⃗</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> </mml:msub> </mml:math> into total <?CDATA $\vec{S}.$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mi>S</mml:mi> <mml:mo>⃗</mml:mo> </mml:mover> <mml:mo>.</mml:mo> </mml:math> Rules based on the string content of a state yield its momentum and asymptotic energy, including the amplitude of the leading ln(L) correction.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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