{"id":"6f508bee-72a4-4757-8f4b-82fc9cc77bd4","arxiv_id":"2602.17656","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Repeated interaction cycles in a 1D Bose gas produce fractional Fermi seas with occupancy 1/(2W+1), whose correlation functions show oscillations and two-power-law decay incompatible with conventional Tomonaga-Luttinger liquid theory.","lead":"This paper predicts that cycling the interactions in a one-dimensional Bose gas from repulsive to attractive and back creates exotic 'fractional Fermi seas' — states filled only to a fraction of the usual Fermi-sea occupancy. It then shows these states have correlation signatures unlike the standard Tomonaga-Luttinger liquid, possibly a new kind of critical phase.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Non-TLL criticality rests on self-consistent power-law fits over a narrow dynamic range; TLL-compatible alternatives are not excluded.","rationale":"The reader's weakest_assumption targets the GHD bound-state/forward-cycle issue, but the paper's treatment of that point is consistent with known results: in the forward direction the g=0 crossing is from attractive to repulsive (where strings are not produced), and the TG-sTG crossing is a standard quench for which continuity of ρ is a well-known description. The numerical extraction of critical exponents and the FO frequency, by contrast, is inherently fragile: N=30 with self-consistent windows and no model selection is insufficient to establish a new critical phase. The reader's overall CONDITIONAL verdict is sound, but for a different primary reason than the stated weakest_assumption; hence 'partial' agreement.","tokens_in":17975,"tokens_out":18542,"duration_ms":186636,"concrete_test":"Using the existing Monte Carlo code (or new runs with N=50,100,200 at fixed density), pre-register a fitting protocol: fix the SD interval to a physical range (e.g., x∈[0.5,2] in units of 1/n) and the LD interval to x∈[10,L/4]; fit g1(x) with (i) A cos(Cx+D)/x^B (bimodal: separate fits in each window), (ii) a single power law with TLL frequency C=2πnW over the full range, and (iii) a two-harmonic TLL form. Compare via AIC/BIC, and extrapolate C and B to L→∞ using a 1/L (or 1/L^2) fit. If the bimodal fit is not preferred, or if C→2πnW as L increases, the non-TLL criticality claim is refuted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of a novel non-TLL critical phase rests on the numerical observation that g(1)(x) exhibits a bimodal power-law decay and a Friedel-oscillation frequency k_FO that departs from 2πnW for W>=1 at γ>0. These observations are extracted from Monte Carlo data with N=L=30 using the fitting procedure described in the Supplemental Material (Sec. 2). The long-distance (LD) fitting window [x̄, x̃] is 'self-consistently' chosen: x̄ is the intersection of the SD and LD power-law envelopes that are themselves outputs of the fits, and x̃ is the position where the envelope reaches |g1|≈10^-3, i.e. the statistical noise floor. This yields only a fraction of a decade of usable LD data, making the fitted LD exponent B_LD and frequency C strongly dependent on the arbitrary interval choice. No alternative decay law (e.g., single power law with subleading harmonic, as expected in a TLL with the natural Fermi wavevector) is tested, and the reported convergence check (N=30 vs N=50, Fig. S3) compares the raw g1(x) curves, not the fitted parameters k_FO, B_SD, B_LD, or x̄. Thus the 'incompatibility with TLL' is not demonstrated: the apparent crossover and frequency shift could be finite-size or fitting artifacts. Because the title and abstract foreground exotic criticality beyond TLL, this is the most load-bearing weakness.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper considers the one-dimensional Lieb-Liniger Bose gas subject to slow cyclic changes of the interaction strength, crossing from repulsive to attractive couplings and back through the TG–sTG transition. Using Generalized Hydrodynamics, the authors derive that after W such cycles an initial ground state is mapped to a GGE with constant occupancy 1/(2W+1) in rapidity space — a 'fractional Fermi sea' (Eq. 3). They then compute the one-particle correlation function g1(x) with a Bethe-ansatz Monte Carlo method and report power-law decay with Friedel oscillations, a crossover between two power laws, and an oscillation frequency that for W≥1 at finite repulsive interaction departs from 2πnW. These features are interpreted as signatures of a critical phase beyond conventional Tomonaga-Luttinger liquid theory, and a companion experimental paper is announced.","tokens_in":18369,"tokens_out":5769,"duration_ms":61117,"significance":"The GHD derivation of the fractional Fermi-sea occupancy is clean, parameter-free, and reproduces the quantum-adiabatic energy results; the entropy jump across the non-interacting point is an elegant and testable consequence. The general idea of realizing effective generalized exclusion statistics with α>1 in a nonequilibrium integrable setting is original and of considerable cold-atom interest. The Monte Carlo method is standard and the paper makes its data available. However, the central claim of non-TLL criticality rests on fits of g1(x) over a narrow dynamic range and on a single-harmonic ansatz; the current numerical evidence does not exclude conventional TLL-compatible alternatives. If the signatures survive more stringent analysis, this would be a substantial result.","major_comments":[{"comment":"The long-distance power-law exponent and the FO frequency are extracted from fits over a window [x̄,x̃] whose right end is set by the statistical noise floor |g1|≈10^-3 (SM Eq. S17 and surrounding text). With N=L=30 this leaves at most a fraction of a decade of usable long-distance data, and the window is selected 'self-consistently' from the fitted envelopes, which risks biasing the exponents. The manuscript does not report the actual fit windows, reduced chi-square, or parameter uncertainties. More importantly, the ansatz A cos(Cx+D)/x^B is imposed without testing alternative decay laws, such as a single power law with subleading harmonics as expected in a TLL. The central claim that the data are 'incompatible with a conventional TLL' is therefore not demonstrated by the presented evidence.","section":"SM Sec. 2 and Fig. 3"},{"comment":"The finite-size check compares raw g1(x) curves for N=30 and N=50, not the fitted parameters (B_SD, B_LD, C, x̄). Two raw curves can overlap while the fitted asymptotic exponents differ, especially when the long-distance window approaches x ~ L/2. To support the power-law and frequency-shift claims, the authors should show the N-dependence of the extracted parameters for at least one representative (γ,W), or provide an independent large-scale method reaching longer distances.","section":"SM Fig. S3"},{"comment":"The departure of the fitted FO frequency from 2πnW is the most direct evidence for non-TLL behavior, but it is obtained from a single-harmonic fit. At g=0 the exact correlation is sin(2πnWx)/(2πnWx), not a pure cos/x^B form, and at finite γ multiple harmonics may be present. A single-harmonic fit to such a function will generically produce an effective frequency C different from the fundamental, without implying a new critical theory. To substantiate the frequency shift, the authors should either extract the oscillation frequency model-independently (e.g., from zero crossings or from the phase of the oscillating envelope) or fit a TLL-inspired multi-harmonic form with the fundamental fixed at 2πnW and show that the data require a different frequency.","section":"Main text Fig. 3(a) and SM Sec. 2"},{"comment":"The GHD derivation of Eq. (3) assumes that no bound states are produced in the forward cycle. The paper justifies this by the divergent binding energy at the TG–sTG transition and by integrability, but the cycle includes a quench through this transition, which is outside the strict slow-driving regime where Euler-scale GHD is proven. The comparison with QA in Fig. 4 is reassuring for energy densities but does not directly constrain string production. A quantitative check of non-adiabatic corrections or of the bound-state population after the quench would make the FFS mapping more robust.","section":"Main text around Eq. (2)"}],"minor_comments":[{"comment":"The caption states 'We show the error bars only for the LD exponent in Panel (b) and x̄ in Panel (a)', but x̄ is plotted in Panel (c), not Panel (a). Please correct the cross-reference.","section":"Fig. 3 caption"},{"comment":"The caption contains a duplicated phrase: 'In Fig. S5. In Fig. S5, we present...' Please remove the repetition.","section":"SM Fig. S5 caption"},{"comment":"The protocol is described as 'slowly and cyclically changed' but also as a 'quench through the TG–sTG transition'. Since GHD validity depends on this distinction, please clarify whether the crossing is instantaneous or performed on a finite timescale.","section":"Main text, introduction"}],"recommendation":"major_revision","confidential_remarks":"The GHD mapping and the FFS concept are likely sound and interesting. The main risk is overinterpretation of the Monte Carlo fits; the authors should be asked to provide model comparison and finite-size scaling of the fitted parameters before the non-TLL criticality claim can be accepted. I did not use the companion experimental paper in this assessment, as it is not part of the submitted manuscript."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new thing here is the GHD derivation of the fractional Fermi sea occupancy, Eq. (3). That derivation is clean: it follows from continuity of the root density when crossing g=0, and it reproduces the earlier quantum adiabatic result without assuming adiabaticity. The accompanying entropy jumps and irreversibility picture are a real addition. If you work on integrable cold-atom systems, this mapping is worth taking seriously, and the occupancy result is likely correct.\n\nThe correlation function part is the soft spot. The paper claims a novel critical phase beyond TLL based on a bimodal power-law decay in g^(1)(x) and a Friedel oscillation frequency that departs from 2π n W at finite γ. But that evidence is numerical, from Monte Carlo with N=30, and the fitting procedure is self-consistent. The long-distance fitting window is less than a decade, and no alternative decay law is tested against the data. The convergence check in Fig. S3 compares raw g^(1)(x) curves, not the fitted exponents or frequencies, so finite-size effects on the fitted parameters are not excluded. The authors themselves say they are arguing for a non-TLL critical field theory rather than presenting one, which is honest but leaves the claim as an interpretation.\n\nThe bound-state suppression argument is plausible and consistent with earlier work, but the quench through the TG–sTG transition is outside the strict slow-driving limit where Euler-scale GHD is proven. That is a minor concern for the occupancy result, since it matches the QA result, but it does mean the protocol's practical validity rests on integrability and the divergent binding energy.\n\nOverall, this is a solid paper on the GHD side and a suggestive but under-supported paper on the criticality side. The data are on Zenodo and the experimental companion is cited as joint submission, so the work is reproducible in principle. I would send it to peer review, but the referees should push for either a thermodynamic-limit extrapolation of the fitted exponents and frequencies, an alternative-fit comparison, or a softened claim about non-TLL criticality. It would also help if the convergence checks were reported for the fitted parameters rather than just the raw curves.\n\nWho gets value from this: people working on GHD, integrable quenches, and cold-atom experiments looking for fractional Fermi seas. The occupancy mapping is the part I'd cite. The criticality claim I'd treat with caution until the numerics are stronger.","headline":"The GHD derivation of fractional Fermi sea occupancy is clean and the result is likely correct, but the claim of non-TLL criticality rests on numerical fits that are not yet convincing; the paper deserves peer review but needs to be tightened.","tokens_in":18880,"tokens_out":1527,"would_cite":true,"duration_ms":16926,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81V70","82B23","82C10"],"pacs":["05.30.-d","67.85.-d","71.10.Pm"],"model":"deepseek-v4-flash","headline":"This paper shows that cyclically ramping the interaction strength of a one-dimensional Bose gas yields fractional Fermi seas — nonequilibrium states with occupancy 1/(2W+1) — whose one-particle correlations display power-law decay and Fried","keywords":["fractional Fermi sea","generalized exclusion statistics","Luttinger liquid","Generalized Hydrodynamics","Lieb-Liniger model","interaction cycles","Friedel oscillations","one-dimensional Bose gas"],"falsifier":"Measure the Friedel frequency after W cycles in a cold-atom experiment: the paper predicts k_FO ≠ 2πnW for any finite repulsive interaction and W≥1; observing k_FO=2πnW, or a single power-law exponent without a crossover, would falsify the fractional-Fermi-sea picture. Alternatively, resolve the rapidity distribution after the cycle: a maximum occupancy above 1/(2W+1) would directly contradict Eq. (3).","tokens_in":17880,"feed_emoji":"⚛️","tokens_out":8901,"duration_ms":73302,"temperature":0.7,"pith_summary":"The paper argues that an integrable one-dimensional Bose gas, driven by slowly cycling its interaction strength from repulsive to attractive and back, does not simply heat up: after W cycles it settles into a nonequilibrium state whose rapidity occupancy is a fractional Fermi sea, 1/(2W+1). These states are described exactly by Generalized Hydrodynamics in the slow-ramp limit, and the cycling acts as a projector onto reduced-occupancy subspaces. The central physical claim is that the one-particle correlation function of these fractional Fermi seas decays as a power law with Friedel oscillations at any finite repulsive interaction, with an oscillation frequency that departs from the expected 2πnW and a crossover between two power laws — properties the paper argues are incompatible with a conventional Luttinger liquid. If right, this opens a route to a new universality class of critical states in one dimension, beyond the Luttinger-liquid paradigm, and is directly testable in cold-atom experiments.","feed_headline":"Cycling interactions creates fractional Fermi seas in a 1D Bose gas","feed_subtitle":"After W cycles, correlations show power-law decay and Friedel oscillations that Luttinger liquid theory cannot explain.","key_machinery":"The central object is the occupancy ϑ(λ)=ρ(λ)/ρ_t(λ), the fraction of available rapidity states actually occupied. The cycle acts as a projector in rapidity space: at each crossing of g=0 from the attractive to the repulsive side, continuity of the root density ρ(λ) forces the occupancy to transform by 1/ϑ_{g=0+,W+1}=2+1/ϑ_{g=0-,W}, so after W cycles a maximally filled Fermi sea becomes one with occupancy 1/(2W+1). Within each branch, the occupancy propagates by the hydrodynamic equation ∂_t ϑ + a_eff ∂_λ ϑ = 0, which conserves the maximum occupancy; this ladder of occupancies converts the initial ground state into a fractional Fermi sea and determines all correlation-function predictions.","core_discovery":"After W forward interaction cycles the initial ground state is mapped to a Generalized Gibbs Ensemble with occupancy ϑ_{g1D,W}(λ)=1/(2W+1) for |λ|<λ_F and zero otherwise (Eq. 3). The paper derives this by solving the Euler-scale hydrodynamics of integrable models with continuity of the root density across the g=0 crossing and across the Tonks-Girardeau to super-Tonks-Girardeau transition, with no bound states generated in the forward direction. In this state, exact Monte Carlo sampling of the integrable eigenstates gives the one-particle correlation function g^(1)(x) for finite repulsive interactions: it shows power-law decay modulated by Friedel oscillations, a crossover from a slower short","pith_inferences":["A natural next step is a field-theoretic description: the paper argues for a 'novel critical phase' but does not construct the effective theory; if the phase is genuine, the bimodal power law and shifted Friedel frequency should emerge from a fixed point with no Luttinger-liquid counterpart.","Because the projection works for arbitrary GGEs and only involves the occupancy, the same cycling protocol could be applied to thermal or finite-density states to produce fractional Fermi seas at nonzero temperature, though temperature may blur the sharp Fermi edge and soften the power laws.","The occupancy mapping predicts that other non-conserved observables, such as the density-density correlation, will also show non-Luttinger signatures since virtual states outside the projected sector contribute; measuring a second correlation function would test whether the phase is truly beyond Luttinger theory or only the one-particle function is anomalous.","The staircase entropy S=n[(1+2W)log(1+2W)−2W log(2W)] provides a state-independent probe of the number of completed cycles; measuring entropy production per cycle in an experiment would verify the projection independently of correlation measurements."],"forward_implications":["After W cycles, any initial GGE is mapped to a GGE with maximum occupancy ≤(2W+1)^{-1}, so the protocol engineers generalized-exclusion-statistics-like states out of equilibrium.","At any repulsive interaction strength, g^(1)(x) shows power-law decay and Friedel oscillations for W≥1, whereas the ground state (W=0) shows a single power law with no appreciable oscillations — the effect is a direct consequence of the fractional Fermi sea.","The Friedel oscillation frequency k_FO deviates from 2πnW as soon as g1D>0 and moves monotonically with the dimensionless coupling γ, giving an experimental observable that distinguishes the phase from a conventional Luttinger liquid.","Within each branch the power-law exponents increase with interaction strength while the crossover distance shrinks; for fixed g1D, larger W reduces the exponents because each cycle pumps energy into kinetic degrees of freedom.","The cycle is irreversible in reverse: crossing g=0 from the repulsive side generates bound states, so fractional Fermi seas form only in the forward direction and the entropy jumps at each crossing."],"fun_headline_variants":["Fractional Fermi seas from interaction cycles in 1D Bose gas","1D Bose gas: fractional Fermi seas from cyclic interactions","Cycling interactions create fractional Fermi seas, beyond Luttinger theory","After W cycles, 1D Bose gas shows fractional Fermi sea criticality","Bose gas cycling yields exotic critical states beyond Luttinger liquids"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The forward ramp never creates bound states: the hydrodynamic calculation assumes the root density stays continuous and that only real rapidities are present when crossing the Tonks-Girardeau–super-Tonks-Girardeau transition, a justification based on the diverging bound-state binding energy at the transition but not on a full treatment of the quench, which lies outside the strict slow-driving limit where Euler-scale hydrodynamics is proven.","fun_headline_variants_meta":{"raw":{"variants":["Fractional Fermi seas from interaction cycles in 1D Bose gas","1D Bose gas: fractional Fermi seas from cyclic interactions","Cycling interactions create fractional Fermi seas, beyond Luttinger theory","After W cycles, 1D Bose gas shows fractional Fermi sea criticality","Bose gas cycling yields exotic critical states beyond Luttinger liquids"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00095,"raw_usage":{"total_tokens":3863,"prompt_tokens":687,"completion_tokens":3176,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":431,"completion_tokens_details":{"reasoning_tokens":3085}},"tokens_in":431,"tokens_out":3176,"duration_ms":19977,"temperature":1.0,"reasoning_tokens":3085,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T22:09:54.294756+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the Friedel frequency after W cycles in a cold-atom experiment: the paper predicts k_FO ≠ 2πnW for any finite repulsive interaction and W≥1; observing k_FO=2πnW, or a single power-law exponent without a crossover, would falsify the fractional-Fermi-sea picture. Alternatively, resolve the rapidity distribution after the cycle: a maximum occupancy above 1/(2W+1) would directly contradict Eq. (3).","supporting_citations":[],"review_version":1}