{"id":"0ca12751-162f-4cad-afee-c254e7ffb8f9","arxiv_id":"2607.01888","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":3.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Exact diagonalization study of trapped bosons finds that stronger interactions and added rotation drive eigenstate delocalization in Fock space, with IPR dropping and Shannon plus von Neumann entropies rising consistently.","lead":"The paper uses exact diagonalization on small numbers of interacting bosons in a harmonic trap to track how interaction strength and rotation change the spread of eigenstates across Fock space. A smart generalist might read it for concrete numerical examples of how multiple entropy measures agree on localization transitions in finite quantum systems.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Finite-size effects in ED limit claims of a true localization-delocalization transition","rationale":"The reader's weakest_assumption correctly isolates the finite-N limitation of ED as the primary uncertainty for the transition claim. This matches the load-bearing issue; the abstract's own remarks on N-dependence reinforce rather than resolve it. No other internal inconsistency (e.g., in the entropy definitions or subspace restriction) appears more central.","tokens_in":1855,"tokens_out":334,"duration_ms":21370,"concrete_test":"For the non-rotating case, recompute IPR vs. interaction strength for all accessible N (e.g., N=3 to N=7) using the same single-particle basis and interaction cutoff; plot the interaction value at which IPR falls to half its non-interacting value versus 1/N and check for convergence to a finite critical point; if the crossing point drifts without bound or the curves fail to sharpen, the transition interpretation is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on exact diagonalization in fixed-Lz subspaces for small boson numbers N, where Hilbert-space dimension grows rapidly. IPR drop and entropy rise with interaction (and further with rotation) are reported, with the effect strengthening for larger N due to bigger basis size. However, no finite-size scaling, data collapse, or extrapolation to N→∞ is performed; the reported saturation at high angular momentum that weakens with N is noted but not quantified via scaling. Without this, the observed changes could be finite-N crossovers rather than a transition whose location or character survives in the thermodynamic limit.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript performs exact diagonalization of a trapped interacting Bose gas within fixed total angular momentum subspaces for small boson numbers N. It reports a localization-delocalization transition in Fock space as interaction strength increases (signaled by decreasing IPR and increasing Shannon and von Neumann entropies), with rotation further promoting delocalization; the effect strengthens with N, and a saturation at high angular momentum weakens with larger N. Three measures are shown to give consistent signals.","tokens_in":1956,"tokens_out":378,"duration_ms":19370,"significance":"If the finite-size observations survive extrapolation, the work supplies a unified numerical characterization of how interaction, rotation, and particle number jointly control Fock-space spreading in small rotating Bose systems, with the internal consistency across IPR, information entropy, and entanglement entropy constituting a strength of the small-system study.","major_comments":[{"comment":"Abstract: the central claim of an interaction-driven localization-delocalization transition (and its further enhancement by rotation) rests on trends observed for small finite N without finite-size scaling, data collapse, or extrapolation to N\to∞; the reported strengthening with N and weakening saturation are noted but not quantified via scaling, leaving open whether the changes are crossovers rather than a transition whose location or character persists in the thermodynamic limit.","section":"Abstract"},{"comment":"Abstract: the statement that 'the effect becomes more pronounced with increasing number of bosons due to the increase of the Hilbert space dimension' is presented as supporting evidence for a transition, yet no systematic study of how the apparent transition point or the saturation regime scales with N is provided, which is load-bearing for interpreting the results as a genuine delocalization transition.","section":"Abstract"}],"minor_comments":[],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading and constructive feedback. We address the major comments point by point below.","responses":[{"response":"The manuscript explicitly studies finite systems, as stated in the title, abstract, and introduction, because exact diagonalization is restricted to small N. We report the observed trends toward delocalization with interaction and rotation, and note that these trends strengthen with N, but we make no claim that the behavior constitutes a transition persisting in the thermodynamic limit. No finite-size scaling or extrapolation is performed. The internal consistency across IPR, Shannon entropy, and von Neumann entropy remains a strength for the accessible sizes. We will revise the abstract to emphasize the finite-N scope and remove any implication of thermodynamic-limit behavior.","revision_made":"partial","referee_comment":"[Abstract] Abstract: the central claim of an interaction-driven localization-delocalization transition (and its further enhancement by rotation) rests on trends observed for small finite N without finite-size scaling, data collapse, or extrapolation to N→∞; the reported strengthening with N and weakening saturation are noted but not quantified via scaling, leaving open whether the changes are crossovers rather than a transition whose location or character persists in the thermodynamic limit."},{"response":"The statement reflects our direct numerical observation that larger N (and thus larger Hilbert-space dimension) permits greater eigenstate spreading. Calculations were performed for multiple N, showing the effect becoming more pronounced. We acknowledge that no systematic scaling analysis of the apparent transition point or saturation regime with N is included. We will revise the abstract to present this as a finite-size observation rather than evidence for a thermodynamic transition.","revision_made":"partial","referee_comment":"[Abstract] Abstract: the statement that 'the effect becomes more pronounced with increasing number of bosons due to the increase of the Hilbert space dimension' is presented as supporting evidence for a transition, yet no systematic study of how the apparent transition point or the saturation regime scales with N is provided, which is load-bearing for interpreting the results as a genuine delocalization transition."}],"tokens_in":1442,"tokens_out":485,"duration_ms":28895,"standing_objections":["Whether the observed trends constitute a true transition whose character persists in the thermodynamic limit, as this requires finite-size scaling and extrapolation to N→∞ beyond the reach of exact diagonalization."]},"desk_editor":{"model":"grok-4.3","letter":"The main point is that this paper runs exact diagonalization in fixed-Lz sectors for small numbers of trapped bosons and tracks ground-state spreading in Fock space with three measures: IPR, Shannon entropy, and von Neumann entropy. Stronger interactions reduce IPR and raise the entropies; adding rotation pushes the same direction, with a saturation at high angular momentum that becomes less pronounced as N grows.\n\nWhat the work does reasonably is show that the three diagnostics move together and that the delocalization signal strengthens with N simply because the basis gets larger. That observation is straightforward and internally consistent for the sizes they can reach.\n\nThe soft spot is exactly the one in the stress-test note. All the reported trends are for very small N where Hilbert-space dimension is manageable. There is no finite-size scaling, no data collapse, and no attempt to extrapolate. The saturation behavior is noted but not quantified with any scaling form, so it is unclear whether the reported localization-delocalization crossover survives or changes character as N increases. Calling the finite-N spreading a “transition” therefore rests on an assumption that the small-system trends are representative, which the data do not test.\n\nThis is for people already working on few-body rotating gases or on Fock-space localization in bosonic systems who want concrete numerical benchmarks for the same measures. A reader outside that narrow slice will not find new methods or broadly applicable results. The calculations look solid within their scope and the authors are honest about the N-dependence they see, so the paper shows clear thinking even if the conclusions are limited by system size.\n\nI would bring it to a reading group only if the group is focused on trapped rotating bosons. I would not cite it in my own work. It is worth sending to peer review in a specialized computational or few-body journal, where referees can check the implementation details and press on the finite-size interpretation.","headline":"Standard small-N ED numerics on rotating bosons; interaction and rotation both increase Fock-space spreading via IPR and entropies, but no scaling means the transition language is overstated.","tokens_in":2454,"tokens_out":462,"would_cite":false,"duration_ms":24944,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Increasing interactions and rotation drive delocalization of eigenstates in the Fock space of trapped bosons.","keywords":["localization-delocalization","trapped bosons","exact diagonalization","Fock space","rotation effects","interaction strength","entanglement entropy","inverse participation ratio"],"falsifier":"Performing the analysis for boson numbers large enough that the saturation effect either persists or disappears entirely would test whether the reported interplay holds.","tokens_in":2730,"feed_emoji":"🌀","tokens_out":667,"duration_ms":26875,"temperature":0.7,"pith_summary":"The paper investigates localization-delocalization transitions in the eigenstates of interacting bosons confined in a trap, both with and without rotation. Using exact diagonalization, it finds that stronger interactions cause eigenstates to spread more widely across the Fock space basis, lowering the inverse participation ratio while raising entropy measures. Rotation further promotes this delocalization, though the effect saturates at high angular momenta in smaller systems. These patterns intensify with more bosons, and delocalized states display stronger entanglement. The study unifies several measures to characterize how interaction, rotation, and particle number control the spread.","feed_headline":"Interactions plus rotation delocalize boson states in Fock space","feed_subtitle":"Exact diagonalization tracks how eigenstate weight spreads with stronger coupling and angular momentum, saturating at high rotation.","key_machinery":"Exact diagonalization within fixed total angular momentum subspaces, using the inverse participation ratio, Shannon entropy, and von Neumann entanglement entropy to quantify the spread of eigenstate weight in Fock space.","core_discovery":"In the non-rotating case, a transition from localized to delocalized behavior is observed with increasing interaction strength. The transition is characterized by a decrease in IPR and a corresponding increase in entropy measures, indicating spread of eigenstate weight over all the basis states in the Hilbert space. In the presence of rotation, the system is driven further toward delocalization. For moderate angular momentum, the eigenstates exhibit partial spreading, while at higher angular momenta a saturation behavior emerges, where further increase in rotation has a limited effect on the localization properties. However, the saturation weakens with increasing system size, indicating a no","pith_inferences":["Rotation could be tuned to control the degree of state delocalization in bosonic many-body systems.","The weakening of saturation with system size suggests that in the large-particle limit rotation may induce complete delocalization without bound.","These findings may connect to questions of ergodicity in rotating quantum gases."],"forward_implications":["The delocalization effect strengthens with increasing boson number due to growth in Hilbert space dimension.","Saturation of delocalization at high rotation becomes less pronounced in larger systems.","Localized states exhibit weaker entanglement while delocalized states show stronger entanglement.","The three measures provide a consistent characterization of the transition."],"fun_headline_variants":["Interaction rotation drives Fock space delocalization in bosons","Rotation further delocalizes interacting boson eigenstates","Delocalized states emerge with stronger interactions and rotation","Saturation in delocalization appears at high angular momentum","Boson entanglement rises with delocalization in Fock space"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The trends seen in small systems with feasible boson numbers reflect the core physics of the transition despite the rapid growth of the Hilbert space with particle number.","fun_headline_variants_meta":{"raw":{"variants":["Interaction rotation drives Fock space delocalization in bosons","Rotation further delocalizes interacting boson eigenstates","Delocalized states emerge with stronger interactions and rotation","Saturation in delocalization appears at high angular momentum","Boson entanglement rises with delocalization in Fock space"]},"model":"grok-4.3","cost_usd":0.008216,"raw_usage":{"total_tokens":3786,"prompt_tokens":784,"num_sources_used":0,"completion_tokens":75,"cost_in_usd_ticks":82162000,"prompt_tokens_details":{"text_tokens":784,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2927,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":784,"tokens_out":75,"duration_ms":28535,"temperature":1.0,"reasoning_tokens":2927,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-03T03:10:58.135313+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Performing the analysis for boson numbers large enough that the saturation effect either persists or disappears entirely would test whether the reported interplay holds.","supporting_citations":[],"review_version":1}