What was already known
Competing low-energy states make the intermediate phase difficult to characterize. The paper compares with earlier numerical work and adds a direct variational spin-gap analysis.
What changed and why it matters
Substantive evidence about an uncertain quantum phase and its gap, extending neural methods beyond reproducing small exactly solvable examples.
The AI contribution
A transformer represents the many-body wave function and is optimized variationally. Human researchers choose the physical model, optimization procedure, observables and finite-size analysis.
Limitations
Initial phase evidence was reported in November 2023; this record uses the expanded April 2025 version, which includes the spin-gap analysis. Variational finite-system calculations and extrapolations support a phase interpretation; they do not prove the infinite-system phase or confirm it experimentally in a material. Competing methods and extrapolation assumptions still matter. AIProofWatch has not reproduced the simulations.
Verification evidence
Evidence labels show what supports the claim. Importance rates its impact if correct.
Author claim
Authors report numerical evidence for the intermediate gapless phase.
Accessible artifact / proof
Methods and analysis are accessible; simulations not reproduced by AIProofWatch.
Peer review
Published in Physical Review B in April 2025. This remains numerical evidence, not an exact phase theorem.
Correction and publication history
Historical addition after primary-source review of statement, baseline, AI attribution and evidence scope. AIProofWatch has not independently verified the result; subscriber alerts disabled.
Read this published revision