{"id":"eefa9842-d091-4265-8159-5c373375ae65","arxiv_id":"2412.17443","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Nonequilibrium Lieb excitations appear in the exact Floquet spectral function of driven Tonks-Girardeau bosons when the mapped fermions form a Floquet-Fermi sea, and become linear across the Brillouin zone at low frequency.","lead":"This paper computes the exact excitation spectrum of a gas of strongly interacting bosons shaken periodically in time. It finds sharp Lieb excitations when the drive starts at a special phase, and shows they become linear across the whole momentum range at low frequency.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Missing convergence study for tcut and epsilon leaves the sharp Lieb peaks in the time-averaged Floquet spectral function unvalidated against finite-time artifacts.","rationale":"The reader's weakest assumption identifies the same load-bearing concern that I find: the numerical convergence in tcut and epsilon is asserted but not demonstrated, and the sharp excitation peaks that constitute the central evidence for nonequilibrium Lieb modes could in principle be finite-time truncation artifacts. The rest of the argument is coherent: the Bose-Fermi mapping for time-dependent Hamiltonians is exact, the Floquet-Lehmann representation is appropriate for the quench protocol, and the FFS mechanism is a plausible explanation of the t0-dependence. The requested convergence study is a concrete, minimal condition that would settle the concern. Since the reader already recommends a conditional acceptance pending such a study, my stress-test does not change the verdict; it reinforces it. I do not see a more serious internal inconsistency or a fatal flaw that would justify rejection or an unverdictable status.","tokens_in":19800,"tokens_out":13831,"duration_ms":146580,"concrete_test":"For the parameters of Fig. 1(b) (Omega=10J, V0=20J, t0^(1)=-751.75T) and Fig. 4(b) (Omega=2.5J, V0=5J), recompute the time-averaged spectral function with tcut multiplied by 2 and by 4, and with epsilon divided by 2, keeping all other parameters fixed. Plot line cuts at fixed quasi-momentum, e.g., q=pi/2 and q=0, and compare the positions, widths, and number of prominent peaks across these runs. Also run with tcut halved to test the opposite limit. If the peak positions shift by more than the linewidth set by epsilon, or if peaks appear or disappear, the asserted independence of tcut and epsilon fails, and the Lieb-mode identification is not yet supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that sharp nonequilibrium Lieb-I and Lieb-II modes emerge for t0=t0^(1) rests on the numerical spectral function A_0(q,omega) = -Im G^R_0(q,omega)/pi, with G^R_0(q,omega) obtained by a Fourier transform over relative time trel truncated at tcut and regularized by a finite epsilon (Supplemental Material, \"Time-dependent Green's function and simulation scheme\"). The authors assert that tcut is chosen sufficiently large and epsilon small enough for convergence, but no convergence data are shown. Because the sharpness and even the existence of peaks can be controlled by the truncation length (Gibbs-type oscillations when tcut*epsilon is not large) or by the broadening width (peak merging when epsilon is too large), the identification of the observed peaks as genuine Lieb excitations is not fully established. The benchmark against the static spectral function in Fig. 1(d) validates the method for the undriven effective Hamiltonian, but it does not validate the t0-dependent nonequilibrium features, since the same tcut/epsilon parameters are used for both. Thus the load-bearing assumption is that the numerical peak structure is converged; without a systematic convergence check, the central claim is not falsifiable against finite-time artifacts.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies a one-dimensional Tonks-Girardeau (TG) gas in an optical lattice under a suddenly switched periodic drive. Using the Bose-Fermi mapping, the authors compute the exact time-averaged Floquet spectral function of the TG gas from time-evolved single-particle orbitals, without an effective-Hamiltonian approximation. They report sharp nonequilibrium Lieb-I and Lieb-II excitations for one representative initial drive time, t0^(1) = -751.75T, attribute their emergence to the formation of a Floquet-Fermi sea in the mapped fermions, and show a qualitatively different, broad spectrum for t0^(2) = -752T. In a low-frequency example (Ω = 2.5J, V0 = 5J), they report linear Lieb excitations extending across nearly the whole Brillouin zone. The Supplemental Material contains the derivation of the determinant formulas for the TG Green's functions, the numerical scheme, and supplementary movies of the t0 dependence.","tokens_in":20024,"tokens_out":6639,"duration_ms":71908,"significance":"If the central claim is correct, this is a valuable contribution: it extends the exact spectral-function method for TG gases to periodically driven systems, covers the low-frequency regime where Magnus expansions are difficult, uses no fitted parameters, and provides a concrete prediction for angle-resolved photoemission experiments with quantum gas microscopes. The static benchmark in Fig. 1(d) and the comparison with the known Lieb-mode structure are genuine strengths. The main weakness is that the sharp nonequilibrium Lieb peaks are established only through a numerical spectral function whose convergence parameters (tcut and epsilon) are not demonstrated, and the central 'Floquet-Fermi sea' criterion is stated purely qualitatively. Both issues are fixable within the manuscript's scope.","major_comments":[{"comment":"The central numerical claim rests on convergence in the relative-time cutoff tcut and the broadening epsilon, but no convergence study is shown. The text asserts that the computed spectral function becomes independent of these parameters (footnote [11]) without displaying data. This matters because A_0(q,ω) is obtained by a Fourier transform truncated at tcut and regularized by a finite epsilon: insufficient tcut*epsilon can produce Gibbs-type oscillations, while overly large epsilon can merge nearby peaks or make broad features appear featureless. Since the sharp Lieb modes in Fig. 1(b) and their absence in Fig. 1(c) are the main results, please report the actual values of tcut and epsilon and show, for representative q and for both t0 values, the convergence of A_0(q,ω) as tcut is increased and epsilon is decreased. Also show that t0 ≈ -752T is far enough into the Floquet regime, e.g., by comparing A_0 for t0 and t0 - T/2 or by scanning |t0|.","section":"Supplemental Material, 'Time-dependent Green's function and simulation scheme', Eqs. (23)-(26) and Fig. 1"},{"comment":"The paper's abstract and conclusion state that nonequilibrium Lieb modes emerge if the underlying mapped fermions form a Floquet-Fermi sea, but the FFS condition is identified only by visual inspection of the imaginary parts of the lesser and greater Green's functions. No quantitative measure is given for 'clear particle and hole separation' versus 'broad and overlapping' occupations, and the approximation pm ≈ δ_m,FFS is not computed from the exact Floquet-state occupations. Because this condition is the proposed organizing principle for the t0 dependence, please define a quantitative FFS diagnostic (for example, the gap between occupied and empty quasi-energy branches, or the overlap between the particle and hole distributions) and evaluate it over the full t0 scan shown in the Supplemental movies. Without such a criterion, the claim that Lieb modes appear exactly when an FFS forms is not falsifiable.","section":"Emergence of nonequilibrium Lieb modes, Figs. 2(a)-(b), 3, and Supplemental movies"},{"comment":"The statement that the linear low-frequency Lieb excitations emerge 'due to the effective many-body interaction mediated by the periodic drive' is not established by the presented analysis. In Fig. 4(a) the mapped noninteracting fermions already display a wide linear dispersion, and the Lieb-I mode of a TG gas is the boundary of the fermionic particle-hole continuum; a linear single-particle band therefore produces a linear lower edge without invoking many-body interactions. To support the interaction-mediation claim, the manuscript should either directly compute the effective interaction terms (e.g., from the higher-order Magnus expansion) or identify a feature in the bosonic spectrum that cannot be understood from the mapped-fermion particle-hole continuum. Otherwise, the claim should be softened to say that the linearization is inherited from the single-particle Floquet spectrum.","section":"Abstract and Conclusion; Fig. 4"}],"minor_comments":[{"comment":"The operator ˆa is described as 'annihilates a single-particle state'; it should be described as a field (annihilation) operator in Fock space, with the matrix elements taken between many-body Floquet states.","section":"Main text, Eqs. (1)-(2)"},{"comment":"The condition 'tcut must be much smaller than t0' is confusing because t0 is negative; write it using absolute values, e.g., tcut ≪ |t0|, and specify the time-ordering constraints for Domain I explicitly.","section":"Supplemental Material, Fig. 1 and surrounding text"},{"comment":"There is a typo 'Floquet-Brilluion zone' in the paragraph discussing Fig. 4(a).","section":"Main text, 'Exact analysis at low-frequency limit'"},{"comment":"The heading 'Acknowldgement' is misspelled and should be 'Acknowledgments'.","section":"Main text, Acknowledgement section"},{"comment":"The notation 'tavg = t' in Eq. (5) is not defined; specify that tavg is the Wigner average time introduced in the Supplemental Material.","section":"Main text, Eq. (5)"},{"comment":"The caption of Fig. 2 is very dense and the main text refers to panels (c)-(e) and (f)-(h) using ranges; labeling each panel explicitly in the caption would improve readability.","section":"Main text, Fig. 2"}],"recommendation":"major_revision","confidential_remarks":"The paper is a good fit for the journal and the exact mapping-based approach is sound in principle. The main risk is not the formalism but the numerical validation: the sharp Lieb peaks and their t0 dependence need a systematic tcut/epsilon convergence study and a quantitative FFS criterion. I do not see any concern about novelty or attribution; the relationship to Settino et al. (PRL 126, 065301) and the earlier Lieb-mode literature is properly acknowledged."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper does something real: it extends the Settino et al. exact spectral function technique to time-periodic drives for a Tonks-Girardeau gas, and shows sharp Lieb-I and Lieb-II modes appear when the mapped fermions occupy a single Floquet–Fermi sea. That is new, and the identification of the Floquet–Fermi sea as the organizing principle is a genuinely useful way to think about Floquet many-body spectra.\n\nThe strength is that the method is exact within the stated lattice model. No fitted parameters, no perturbative approximation; the spectral functions are computed from time-evolved single-particle orbitals via the Bose–Fermi mapping. The high-frequency results match the effective Hamiltonian, which is a good sanity check. The low-frequency regime, where the bosonic Lieb modes become linear across most of the Brillouin zone while the mapped fermions have a Dirac-like dispersion, is a concrete prediction that goes beyond any Magnus expansion. I also appreciate that the t0-dependence is handled honestly: the paper scans t0 rather than choosing it to force a desired spectrum, and the FFS is diagnosed from the lesser/greater Green's functions independently of the excitation peaks.\n\nThe soft spots are mostly about presentation and verification. The supplemental material states that the spectral function is independent of the cutoff tcut and broadening epsilon, but no convergence data are shown. That is a legitimate referee request, and the stress-test note is right to flag it. I do not think it is load-bearing: the static benchmark in Fig. 1(d) and the t0-dependence movies in the supplement make a finite-time artifact less likely, but the authors should show a convergence plot (e.g., peak sharpness vs. tcut and epsilon) before I would be fully comfortable. Second, the Floquet–Fermi sea is defined operationally from the particle–hole separation; a brief formal definition or a statement of how it is extracted would strengthen the paper. Third, the phrase \"effective many-body interactions mediated by the external periodic drive\" in the low-frequency discussion is misleading: the mapped fermions remain noninteracting, and the linearization is a single-particle Floquet effect. That language should be toned down.\n\nThe citation pattern looks fine; Settino et al. is properly credited, and the self-citation to He et al. is relevant and not self-promotional.\n\nWho is this for? People working on exact nonequilibrium spectral functions, Floquet engineering of ultracold gases, and integrable models out of equilibrium. It deserves a serious referee, not a desk reject. My recommendation: accept after minor revision, provided the authors supply the convergence study and tighten the interaction language.","headline":"Exact Floquet spectral functions for a driven Tonks-Girardeau gas with a new Floquet-Fermi sea mechanism; a solid paper that needs a convergence study before acceptance.","tokens_in":20599,"tokens_out":1677,"would_cite":true,"duration_ms":18209,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["67.85.-d","05.30.Jp"],"model":"deepseek-v4-flash","headline":"This paper claims that a periodically driven Tonks-Girardeau gas exhibits exact nonequilibrium Lieb-I and Lieb-II excitations whenever the initial drive phase makes the mapped fermions occupy a single Floquet-Fermi sea, with low-frequency…","keywords":["Tonks-Girardeau gas","Floquet spectral function","Lieb excitations","Bose-Fermi mapping","periodic driving","Floquet-Fermi sea","low-frequency driving","nonequilibrium spectral function"],"falsifier":"Repeat the numerical spectral function for the same parameters while progressively increasing the relative-time cutoff $t_{\\mathrm{cut}}$ and decreasing the broadening $\\epsilon$; if the sharp Lieb peaks shift, change weight, or disappear, the claimed nonequilibrium modes are artifacts of the finite simulation window.","tokens_in":19567,"feed_emoji":"⚛️","tokens_out":8411,"duration_ms":69099,"temperature":0.7,"pith_summary":"The paper analyzes a one-dimensional gas of strongly interacting Tonks-Girardeau bosons in an optical lattice when a strong periodic drive is suddenly switched on. It claims that the exact time-averaged Floquet spectral function of the gas develops sharp nonequilibrium Lieb-I and Lieb-II excitation branches, but only when the initial phase of the drive is such that the mapped noninteracting fermions fill a single Floquet-Fermi sea, $p_m \\approx \\delta_{m,\\mathrm{FFS}}$. When that condition fails, the excitation spectrum becomes broad and featureless. In the low-frequency regime, the exact calculation shows the Lieb branches becoming linear across almost the entire Brillouin zone while the mapped fermions develop a wide Dirac-like linear dispersion. If correct, this gives an exact, parameter-free window into driven strongly correlated bosons without relying on an effective static Hamiltonian.","feed_headline":"Sharp Lieb modes emerge in a periodically driven boson gas","feed_subtitle":"When the drive's starting phase fills a Floquet-Fermi sea, the exact spectrum shows linear Lieb excitations.","key_machinery":"The central object is the time-averaged Floquet spectral function $A_\\ell(\\omega) = -(1/\\pi)\\,\\mathrm{Im}\\,G^R_\\ell(\\omega)$, built from the Lehmann representation of the lesser and greater Green's functions together with the exact determinant formulas for the Tonks-Girardeau Green's functions obtained through the Bose-Fermi mapping. The load-bearing condition is the formation of a Floquet-Fermi sea, meaning the occupations $p_m(t_0)$ of the many-body Floquet states reduce to $\\delta_{m,\\mathrm{FFS}}$; this condition, controlled by the initial drive phase $t_0$, is what selects sharp Lieb-I and Lieb-II peaks. The exactness comes from computing the Green's functions directly from time-evolved single-particle fermionic orbitals, with no effective static Hamiltonian used anywhere in the derivation.","core_discovery":"By combining the Bose-Fermi mapping theorem with the Lehmann representation of the Floquet Green's function, the paper derives the exact time-averaged spectral function of the driven Tonks-Girardeau gas and identifies its sharp peaks with the Lieb-I and Lieb-II branches, the two boundary branches of particle-hole excitations of the one-dimensional Bose gas. The appearance of these peaks is governed by the occupations of the many-body Floquet states: when the drive starts at a phase such that the mapped fermions occupy a single Floquet-Fermi sea state, $p_m \\approx \\delta_{m,\\mathrm{FFS}}$, the spectral function acquires poles at $E_m - E_{\\mathrm{FFS}}$ and sharp Lieb modes emerge. For other starting phases the occupations of many Floquet states mix, no Fermi sea forms, and the spectrum broadens. In the low-frequency regime, where effective Hamiltonians from high-frequency expansions are not reliable, the exact spectral function reveals linear Lieb modes extending over nearly the whole first Brillouin zone, which the paper attributes to effective many-body interactions generated by the periodic drive rather than to the single-particle band structure alone.","pith_inferences":["A natural experimental test would be to scan the initial drive phase $t_0$ continuously: the predicted sharp transition from well-defined Lieb modes to a broad spectrum whenever the Floquet-Fermi sea is lost is a distinctive, easy-to-look-for signature.","The same Floquet-Fermi-sea criterion is likely to control sharp spectral features in other exactly solvable one-dimensional models, such as hard-core anyons or the strongly interacting Hubbard model, where exact Green's functions are available.","If the low-frequency linearization survives finite-size and finite-temperature checks, it suggests a way to Floquet-engineer ballistic transport in strongly interacting bosonic systems without relying on special lattice geometries."],"forward_implications":["The nonequilibrium Lieb modes are properties of the driven many-body bosonic system and not of the mapped noninteracting fermions, since the fermionic spectral function shows a two-band quasi-energy spectrum while the bosonic one displays the Lieb-I, Lieb-II, and upper lattice branches.","Because the calculation is exact, the same approach covers arbitrarily low driving frequencies and strong drives, including regimes where Magnus or high-frequency expansions are uncontrolled.","The low-frequency linearization of the Lieb modes means many excitations share the same phase velocity, which the paper suggests could enhance mobility and be relevant for atomtronic devices.","The predicted sharp Lieb peaks and their linear dispersion are in principle observable with time-resolved photoemission spectroscopy implemented through quantum gas microscopes."],"supporting_citations":[{"why":"Supplies the Bose-Fermi mapping that reduces the Tonks-Girardeau gas to noninteracting fermions, the foundation of the exact treatment.","marker":"[25]"},{"why":"Provides the exact spectral function method for a Tonks-Girardeau gas in a lattice that the paper extends to time-dependent driving.","marker":"[27]"},{"why":"Gives the Lehmann representation for Floquet Green's functions and the positivity conditions used to define the spectral function.","marker":"[31]"},{"why":"Establishes the stroboscopic versus nonstroboscopic dynamics and supplies the effective-Hamiltonian benchmark in the high-frequency limit.","marker":"[1]"},{"why":"Sets up the Floquet theory and the gauge transformation used to write the driven lattice model.","marker":"[2]"},{"why":"Supplies the two-band dimerized dispersion used to identify the effective band structure of the mapped fermions.","marker":"[39]"}],"fun_headline_variants":["Drive-induced Lieb modes emerge in boson gas","Floquet-Fermi sea unlocks sharp Lieb excitations","Periodic drive yields linear Lieb spectrum","Exact solution exposes driven Lieb modes","Boson gas drive reveals Lieb branches"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central claim rests on the assumption that the finite relative-time cutoff $t_{\\mathrm{cut}}$ and the broadening $\\epsilon$ used in the numerical Fourier transform are at convergence, so the sharp peaks are genuine Floquet Lieb modes rather than finite-time artifacts.","fun_headline_variants_meta":{"raw":{"variants":["Drive-induced Lieb modes emerge in boson gas","Floquet-Fermi sea unlocks sharp Lieb excitations","Periodic drive yields linear Lieb spectrum","Exact solution exposes driven Lieb modes","Boson gas drive reveals Lieb branches"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000223,"raw_usage":{"total_tokens":1423,"prompt_tokens":880,"completion_tokens":543,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":496,"completion_tokens_details":{"reasoning_tokens":470}},"tokens_in":496,"tokens_out":543,"duration_ms":5407,"temperature":1.0,"reasoning_tokens":470,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T05:27:05.698185+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the numerical spectral function for the same parameters while progressively increasing the relative-time cutoff $t_{\\mathrm{cut}}$ and decreasing the broadening $\\epsilon$; if the sharp Lieb peaks shift, change weight, or disappear, the claimed nonequilibrium modes are artifacts of the finite simulation window.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the Lehmann representation for Floquet Green's functions and the positivity conditions used to define the spectral function."},{"cited_title":"Bukov and A","cited_arxiv_id":null,"evidence_quote":"Establishes the stroboscopic versus nonstroboscopic dynamics and supplies the effective-Hamiltonian benchmark in the high-frequency limit."}],"review_version":1}