Gapped spin liquid with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> topological order for the kagome Heisenberg model
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Bibliographic record
Abstract
We apply the symmetric tensor network state (TNS) to study the nearest-neighbor spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice. Our method keeps track of the global and gauge symmetries in the TNS update procedure and in tensor renormalization group (TRG) calculations. We also introduce a very sensitive probe for the gap of the ground state---the modular matrices, which can also determine the topological order if the ground state is gapped. We find that the ground state of the Heisenberg model on the kagome lattice is a gapped spin liquid with the ${\mathbb{Z}}_{2}$ topological order (or toric code type), which has a long correlation length $\ensuremath{\xi}\ensuremath{\sim}10$ unit cells. We justify that the TRG method can handle very large systems with thousands of spins. Such a long $\ensuremath{\xi}$ explains the gapless behaviors observed in simulations on smaller systems with less than 300 spins or shorter than the length of 10 unit cells. We also discuss experimental implications of the topological excitations encoded in our symmetric tensors.
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Full frame distilled prediction
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.003 |
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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