{"id":"921826f2-33a8-4a2a-8733-cd738eefe4a5","arxiv_id":"2605.28861","paper_version":1,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Single-spin-flip Metropolis-Hastings sampling breaks ergodicity and produces artifactually low energies in neural network studies of the kagome antiferromagnet, so the claimed spinon pair-density-wave ground state is unsupported.","lead":"This comment shows that low variational energies reported for the kagome Heisenberg antiferromagnet using neural networks stem from non-ergodic sampling with single-spin-flip updates that freeze the Markov chains. A smart generalist might read it to understand why machine learning methods for quantum systems require careful validation of sampling procedures against established benchmarks like DMRG.","discovery_kind":"replication","skeptic_critique":{"model":"grok-4.3","headline":"Spin-exchange updates may leave residual non-ergodicity on N=108, so the NN variational minimum could remain unexplored and the energy comparison to DMRG inconclusive.","rationale":"The load-bearing point identified above is identical to the reader's weakest_assumption. No additional internal inconsistency, missing control, or unsupported step appears in the argument as summarized.","tokens_in":1721,"tokens_out":313,"duration_ms":51324,"concrete_test":"Run at least three independent optimizations on the N=108 cluster using spin-exchange updates, each starting from a different random seed and with at least 10x the reported number of sweeps; if any run produces an energy more than 0.5% lower than the others while maintaining the same NN architecture, the ergodicity assumption is insufficient.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The comment's central claim requires that spin-exchange updates render the Metropolis-Hastings chain ergodic enough for the group-equivariant NN to reach its true variational minimum on the N=108 cluster. If autocorrelation times remain long (as is common for local updates in frustrated magnets), independent runs or longer trajectories could still yield biased energies. In that case the observation of energies higher than DMRG would not demonstrate that the ansatz cannot support states below DMRG; it would only show that the particular optimization trajectory did not locate them. This directly affects part (ii) of the claim and therefore the conclusion that the original low energies were purely sampling artifacts.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript is a comment arguing that the low variational energies obtained by group-equivariant convolutional neural networks for the spin-1/2 kagome Heisenberg antiferromagnet on the N=108 cluster (reported in Phys. Rev. X 15, 011047 (2025)) are artifacts of broken ergodicity under single-spin-flip Metropolis-Hastings updates. It further claims that replacing these with spin-exchange updates produces energies significantly above existing DMRG benchmarks, thereby undermining the original identification of a spinon pair-density-wave ground state.","tokens_in":1861,"tokens_out":407,"duration_ms":31326,"significance":"If the central claims hold, the comment would establish that standard single-spin-flip sampling is inadequate for neural-network variational Monte Carlo on frustrated magnets and would restore consistency with DMRG results, thereby affecting the interpretation of the kagome ground state. The work draws on textbook Markov-chain properties and external DMRG benchmarks without introducing fitted parameters.","major_comments":[{"comment":"Abstract: the claim that spin-exchange updates render the Metropolis-Hastings chain ergodic enough for the neural-network ansatz to reach its true variational minimum on N=108 is not accompanied by quantitative diagnostics (autocorrelation times, integrated autocorrelation lengths, or convergence statistics from independent initializations). Without these, the reported energies higher than DMRG could still reflect residual sampling bias rather than an intrinsic limitation of the ansatz.","section":"Abstract"},{"comment":"The manuscript contrasts the two update rules and reports the resulting energy discrepancy, but does not demonstrate that the single-spin-flip chains are demonstrably frozen (e.g., via acceptance-rate collapse or trapped magnetization sectors) on the specific N=108 cluster; this leaves the attribution of the original low energies as purely an ergodicity artifact partially unanchored.","section":"Abstract"}],"minor_comments":[],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful reading of our comment. We address the two major comments point by point below, indicating where we agree that additional material would strengthen the presentation and where we maintain that the existing evidence is sufficient.","responses":[{"response":"We agree that explicit autocorrelation diagnostics would add quantitative support. The energy difference we report (well above DMRG benchmarks) is already inconsistent with residual bias under spin-exchange updates, given that the neural-network ansatz is variationally bounded from below. In revision we will add a short paragraph reporting integrated autocorrelation lengths and results from independent initializations on the N=108 cluster to make this explicit.","revision_made":"partial","referee_comment":"[Abstract] Abstract: the claim that spin-exchange updates render the Metropolis-Hastings chain ergodic enough for the neural-network ansatz to reach its true variational minimum on N=108 is not accompanied by quantitative diagnostics (autocorrelation times, integrated autocorrelation lengths, or convergence statistics from independent initializations). Without these, the reported energies higher than DMRG could still reflect residual sampling bias rather than an intrinsic limitation of the ansatz."},{"response":"The primary evidence for freezing remains the unphysical result that single-spin-flip sampling produces variational energies below all published DMRG values on the same cluster; a correctly sampled variational wave function cannot do so. While direct acceptance-rate or sector-trapping data for the original N=108 runs are not reproduced in our comment (as they were not reported in the target paper), the systematic energy lowering with single-spin-flip updates across multiple neural-network architectures is the expected signature of broken ergodicity in frustrated magnets. We will add a concise paragraph recalling this textbook diagnostic in the revised manuscript.","revision_made":"partial","referee_comment":"[Abstract] The manuscript contrasts the two update rules and reports the resulting energy discrepancy, but does not demonstrate that the single-spin-flip chains are demonstrably frozen (e.g., via acceptance-rate collapse or trapped magnetization sectors) on the specific N=108 cluster; this leaves the attribution of the original low energies as purely an ergodicity artifact partially unanchored."}],"tokens_in":1369,"tokens_out":467,"duration_ms":39902,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"This comment flags a methodological problem in the recent PRX paper on the kagome Heisenberg antiferromagnet. The original work used group-equivariant neural networks and reported variational energies below DMRG on the N=108 cluster, leading to a spinon pair-density-wave claim. The comment demonstrates that single-spin-flip updates freeze the Markov chains in this frustrated system, violating the ergodicity needed for Metropolis-Hastings to reach the true variational minimum.\n\nWhat stands out is the direct application of standard MCMC requirements and the side-by-side energy comparison to existing DMRG benchmarks on the same cluster. That comparison is external and reproducible, and the demonstration that spin-exchange updates raise the energies is new for this specific ansatz. The logic follows textbook properties of Markov chains without circular fitting.\n\nA soft spot is whether spin-exchange updates fully eliminate bias on N=108. Local updates in frustrated magnets often have long autocorrelation times, and the comment does not report mixing diagnostics or multiple independent runs. If residual non-ergodicity remains, the higher energies show only that those particular trajectories missed lower states, not that the ansatz cannot reach them. The discrepancy with DMRG is large, so the main artifact claim still holds, but the conclusion that the original energies were purely sampling artifacts is slightly stronger than the evidence presented.\n\nThis paper is for people working on variational Monte Carlo or neural-network ansatzes for quantum magnets, especially those studying the kagome model. It serves as a practical warning about update rules. It deserves a serious referee because it directly challenges a high-profile ground-state identification with a fix that can be checked against published DMRG data.\n\nI would send it for peer review.","headline":"This comment shows the original NN paper's low energies on the kagome model were sampling artifacts from non-ergodic single-spin flips, with proper updates giving higher energies than DMRG.","tokens_in":2359,"tokens_out":432,"would_cite":true,"duration_ms":25826,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Low energies reported for kagome magnet neural network arise from frozen Markov chains in sampling.","keywords":["kagome Heisenberg antiferromagnet","neural network variational Monte Carlo","ergodicity","Metropolis-Hastings sampling","spinon pair-density-wave","DMRG","spin liquid","Markov chain"],"falsifier":"A side-by-side comparison, on smaller clusters with known exact energies, of the minimum reached by the identical neural network when using single-spin-flip updates versus spin-exchange updates.","tokens_in":2628,"feed_emoji":"","tokens_out":701,"duration_ms":45686,"temperature":0.7,"pith_summary":"This comment paper examines a recent neural-network variational Monte Carlo study that reported energies for the spin-1/2 kagome Heisenberg antiferromagnet lower than density matrix renormalization group benchmarks and identified a spinon pair-density-wave ground state on the N=108 cluster. The analysis shows that the single-spin-flip update rule in the Metropolis-Hastings sampler traps the Markov chains and prevents full exploration of spin configurations. Replacing that rule with spin-exchange updates restores ergodicity and drives the neural network to energies above the DMRG values. The discrepancy indicates that the reported low-energy state is an artifact rather than a true variational minimum.","feed_headline":"Sampling flaw invalidates neural net kagome ground state claim","feed_subtitle":"Single-spin-flip updates trap chains in artificial minima; spin-exchange updates produce energies above DMRG benchmarks on the N=108 cluster","key_machinery":"Ergodicity of the Markov chain in Metropolis-Hastings sampling for neural-network wave functions, controlled by the choice between single-spin-flip and spin-exchange local updates.","core_discovery":"The variational energies reported in the original work are artifacts of broken ergodicity in the Metropolis-Hastings sampling with single-spin-flip updates; when ergodic sampling is enforced via spin-exchange updates, the neural network converges to energies significantly higher than existing DMRG results.","pith_inferences":["Similar ergodicity problems are likely to appear in other variational Monte Carlo applications to frustrated spin models where configuration space is constrained.","Studies using neural-network ansatzes should routinely compare results across independent update families to confirm that reported minima are not local.","The gap between neural-network and DMRG energies after ergodicity correction may reflect limits in the expressivity of the chosen network architecture or in the optimization procedure itself.","This example underscores the value of testing sampling procedures on benchmark clusters where exact or near-exact references exist."],"forward_implications":["The spinon pair-density-wave state is not supported as the ground state of the neural-network ansatz under ergodic sampling.","Density matrix renormalization group calculations remain the lowest variational upper bounds obtained so far for this system size.","Neural-network variational Monte Carlo studies of quantum magnets require explicit checks that the chosen update rule produces ergodic chains.","Machine-learning claims of new ground-state phases must be cross-validated with multiple sampling schemes before they can be considered reliable."],"fun_headline_variants":["Kagome ML claim fails ergodicity test","Neural net kagome energies rise with ergodic updates","Spin-exchange fixes show kagome ML energies above DMRG","Nonergodic sampling invalidates kagome spinon wave result"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"Spin-exchange updates achieve sufficient ergodicity on the N=108 cluster to reach the true variational minimum of the neural-network ansatz.","fun_headline_variants_meta":{"raw":{"variants":["Kagome ML claim fails ergodicity test","Neural net kagome energies rise with ergodic updates","Spin-exchange fixes show kagome ML energies above DMRG","Nonergodic sampling invalidates kagome spinon wave result"]},"model":"grok-4.3","cost_usd":0.004112,"raw_usage":{"total_tokens":1978,"prompt_tokens":613,"num_sources_used":0,"completion_tokens":67,"cost_in_usd_ticks":41115500,"prompt_tokens_details":{"text_tokens":613,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1298,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":613,"tokens_out":67,"duration_ms":15975,"temperature":1.0,"reasoning_tokens":1298,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-30T15:50:31.670485+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A side-by-side comparison, on smaller clusters with known exact energies, of the minimum reached by the identical neural network when using single-spin-flip updates versus spin-exchange updates.","supporting_citations":[],"review_version":1}