Magnetization Plateau of the<i>S</i>= 1/2 Frustrated Heisenberg Chain with Period 3 Parity Invariant Exchange Modulation
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Bibliographic record
Abstract
The magnetization plateau of the S = 1/2 frustrated Heisenberg chain with period 3 parity invariant exchange modulation is investigated by the bosonization and numerical exact diagonalization method. The ground state phase diagram at 1/3 of the saturated magnetization is obtained. Among three degenerate ↑↑↓-type plateau states in the uniform chain, two of them (↓↑↑↓↑↑⋅⋅⋅ and ↑↓↑↑↓↑⋅⋅⋅) turned out to be robust against the period 3 exchange modulation which favors the phase up to a critical value of the modulation amplitude ( = singlet dimer) resulting in the Z2 symmetry broken phase. Another ↑↑↓-type state with ↑↑↓↑↑↓⋅⋅⋅ configuration is stabilized for period 3 modulation with opposite sign. The transition between the -phase and Z2-broken phase is the Ising transition and that between the ↑↑↓↑↑↓⋅⋅⋅ -phase and Z2 broken phase is the first order transition. The spin configuration in each phase is numerically verified by applying the local symmetry breaking field.
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Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
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 | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
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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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