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Exotic critical states as fractional Fermi seas in the one-dimensional Bose gas

T0 review · 4 major / 3 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read 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

desk verdict 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. read the letter →

arxiv 2602.17656 v2 pith:THXHZLCQ submitted 2026-02-19 cond-mat.quant-gas cond-mat.stat-mechquant-ph

Alvise Bastianello , Yi Zeng , Sudipta Dhar , Zekui Wang , Xudong Yu , Milena Horvath , Grigori E. Astrakharchik , Yanliang Guo
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Hanns-Christoph Nägerl Manuele Landini
This is my paper · ORCID
classification cond-mat.quant-gascond-mat.stat-mechquant-ph MSC 81V7082B2382C10 PACS 05.30.-d67.85.-d71.10.Pm
keywords fractionalFermiseageneralizedexclusionstatisticsLuttingerliquidHydrodynamicsLieb-LinigermodelinteractioncyclesFriedeloscillationsone-dimensionalBosegas
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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).

Watch

Extended reading notes

Core claim

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

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 3 minor

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.

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 (4)
  1. [SM Sec. 2 and Fig. 3] 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.
  2. [SM Fig. S3] 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.
  3. [Main text Fig. 3(a) and SM Sec. 2] 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.
  4. [Main text around Eq. (2)] 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.
minor comments (3)
  1. [Fig. 3 caption] 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.
  2. [SM Fig. S5 caption] The caption contains a duplicated phrase: 'In Fig. S5. In Fig. S5, we present...' Please remove the repetition.
  3. [Main text, introduction] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: FFS occupancy follows from GHD continuity; correlation exponents are data diagnostics, not fitted inputs.

full rationale

The central prediction, the fractional Fermi sea occupancy ϑ_{g1D,W}(λ)=1/(2W+1) in Eq. (3), is derived from the GHD continuity condition at the non-interacting point. The paper explicitly derives the recursion 1/ϑ_{0+,W+1}=2+1/ϑ_{0−,W} from continuity of the root density ρ(λ), and starting from the ground-state occupancy ϑ=1 this yields the reduced occupancy after W cycles. This is an analytical consequence of the stated GHD equations, not a fitted parameter or a quantity defined in terms of the final correlations. The one-particle correlation function is then computed by Monte Carlo sampling of the Bethe-ansatz form factors on the GGE determined by that occupancy, and the power-law exponents and Friedel-oscillation frequency are extracted from the resulting g(1)(x). These fitted quantities are diagnostics of the computed state, not inputs used to define the state. The agreement with the quantum-adiabatic results of Refs. [13,14] is presented as a consistency check, not as the derivation itself. The no-bound-state assumption in the forward cycle is an explicit physical assumption supported by prior work, and the self-consistent fitting-window procedure in the Supplemental Material concerns the statistical extraction of exponents from Monte Carlo data; it is a robustness/correctness concern, not a circular reduction of the theoretical claim. No load-bearing step equates a fitted input with a prediction or defines the target result in terms of itself.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

The central FFS occupancy is derived, not fitted; the fitted parameters are the correlation-function exponents and frequencies that constitute the evidence for the novel criticality. The paper's assumptions are standard GHD ingredients plus an assumed power-law decay form.

free parameters (3)
  • Power-law exponents B_SD, B_LD (per γ, W) = Fig. 3(b)
    Exponents extracted by fitting A·cos(Cx+D)/x^B to Monte Carlo g(1)(x); the claim of bi-modal power-law criticality rests on these fits.
  • FO frequency C (per γ, W) = Fig. 3(a)
    Fitted oscillation frequency; its departure from 2πnW is the central evidence against TLL.
  • Crossover distance x̄ = Fig. 3(c)
    Defined as the intersection of the SD and LD power-law fits; used to justify two separate power-law regimes.
assumptions (5)
  • domain assumption Euler-scale GHD (Eq. 2) describes the cyclic protocol, including the sudden TG–sTG quench via continuity of ρ(λ)
    GHD validity for slow driving is standard; the extension to the quench is argued but not derived in this Letter.
  • domain assumption No bound states form in the forward attractive branch; the real-rapidity sector is sufficient
    Assumed from integrability and prior works [18-20,34,48,49]; failure would change the FFS mapping and the entropy staircase.
  • domain assumption Thermodynamic limit is reached at N=30, L=30
    Convergence checked against N=50 for selected parameters (SM Fig. S3), but not for all reported (γ,W).
  • standard math Monte Carlo form factors from Ref. [54] and the sampling scheme of Ref. [53] are correct
    Used to compute g(1)(x); no independent check of the determinant formulas is provided in this paper.
  • ad hoc to paper Power-law ansatz A·cos(Cx+D)/x^B for g(1)(x) in FFS states
    Assumed fitting form; no first-principles derivation that the true decay is power-law rather than, e.g., exponential times an oscillatory factor at finite γ.
invented entities (1)
  • Non-TLL critical field theory (suggested)
    purpose: Postulated underlying field theory for the observed bi-modal power-law correlations in FFS
    No explicit theory is constructed; the claim is inferred from numerical fits. There is no falsifiable handle outside the numerics presented.

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Pith. "Pith review of Exotic critical states as fractional Fermi seas in the one-dimensional Bose gas." pith.science (2026). https://pith.science/paper/THXHZLCQ

@misc{pith2026260217656,
  author       = {Pith},
  title        = {Pith review of: Exotic critical states as fractional Fermi seas in the one-dimensional Bose gas},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/THXHZLCQ}},
  note         = {Machine review of arXiv:2602.17656}
}
read the original abstract

Critical quantum field theories occupy a central position in modern theoretical physics for their inherent universality stemming from long-range correlations. As an example, the Tomonaga-Luttinger liquid (TLL) describes a wealth of one-dimensional quantum systems at low temperatures. Its behavior is deeply rooted in the emergence of an effective Fermi sea, leading to power-law correlations and Friedel oscillations. A promising direction to realize systems exhibiting novel universal behavior beyond TLL is through the generalization of the underlying Fermi sea. In this Letter, we show that fractional Fermi seas with reduced occupancy arise in an integrable Bose gas driven out of equilibrium by cyclic changes in interactions from repulsive to attractive. The correlation functions feature signatures of criticality incompatible with a conventional TLL, suggesting a novel critical phase. Our predictions, based on Generalized Hydrodynamics, are directly relevant to cold atoms.

Figures

Figures reproduced from arXiv: 2602.17656 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. overviews the observed power-law expo￾nents and FO. The oscillation frequency kFO ( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

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    The F orm F actor The determinant form for the form factor∣⟨{µ j}N−1 ℓ=1 ∣ ˆψ(0)∣{λj}N j=1⟩∣2 has been computed in Ref. [54] as (below, c≡mg 1D/̵h2) ∣⟨{µj}N−1 ℓ=1 ∣ ˆψ(0)∣{λj}N j=1⟩∣2 =c 2N−1 ∏N j>k=1((λj−λ k)2+c 2)2 ∏N a=1 ∏N−1 b=1 (λa−µ b)2 detU({µ i}N−1 i=1 ,{λ j}N j=1) ∣∣{...

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