{"id":"e9b2c9ae-09a3-4461-b153-793d74eed409","arxiv_id":"1908.08515","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":8,"one_line_summary":"Using entropy-shuttling narrow bands, the authors prepare cold photo-doped, negative-temperature superconducting, and eta-paired nonequilibrium states of the Hubbard model within nonequilibrium DMFT.","lead":"This paper shows in simulations that a cooling-by-doping trick, moving entropy into narrow helper bands, can prepare cold and unusual states of the Hubbard model. These include a photo-doped Mott insulator with a sharp metallic response, a repulsive-model superconductor with inverted population, and a long-lived eta-paired superconducting state.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claims rest on the NCA impurity solver without an exact-solver cross-check; the reported order parameters and effective temperatures could be solver artifacts.","rationale":"The reader's weakest_assumption correctly identifies the NCA solver as the most load-bearing element of the paper. The new physics claims — cooling to low effective temperatures, the negative-temperature s-wave superconducting state, and the eta-paired state — are all demonstrated only within DMFT+ NCA. Because NCA is an approximate impurity solver with known quantitative limitations in low-temperature and symmetry-broken regimes, the central quantitative statements are not yet independently secured. The paper contains no numerical comparison of the new cooling-by-doping protocols against an exact or higher-order solver; the only internal check (Fig. 3) compares two NCA calculations, so it cannot resolve this concern. The exact-solver reference in Ref. 48 supports the population-inversion mechanism but not the specific cooling efficiencies and order parameters reported here. I do not see an internal inconsistency in the paper; the issue is a correctness risk, not a soundness failure. The paper is transparent about its proof-of-principles scope and does not overstate its conclusions. A conditional acceptance with the requested cross-check and error estimation is therefore the appropriate verdict, and my stress-test does not change that assessment. If such a cross-check were to show that the NCA results are qualitatively stable, the paper's central claim would be substantially strengthened.","tokens_in":14707,"tokens_out":7179,"duration_ms":87104,"concrete_test":"Rerun at least one central protocol, preferably the negative-temperature s-wave state of Fig. 5, with an independent impurity solver that is reliable in the symmetry-broken low-temperature regime, such as time-dependent exact diagonalization with a finite bath or the one-crossing approximation. Compare the time-resolved superconducting order parameter, double occupation, and the fitted beta_eff after decoupling; if the order parameter changes by more than about 10% or beta_eff shifts by more than about 1, the NCA results are not quantitatively robust, whereas agreement would settle the solver-dependence concern.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section II states that all impurity-model solutions use the non-crossing approximation (NCA). The paper's headline results — the conductivity match at beta_eff = 19.2, 14.4, and 13 (Fig. 2), the s-wave superconducting order parameter of magnitude ~0.36 after thermalization to beta = -7.3 (Fig. 5), and the eta-pairing order parameter ~0.4 (Figs. 6 and 7) — are all produced with this single approximate solver. NCA is uncontrolled in precisely the regimes these claims occupy: low effective temperature near a Fermi-liquid/superconducting instability, and symmetry-broken phases with anomalous Green's functions. The only internal cross-check in Sec. III B compares an AC-field quench with an equivalent U-quench, but both are computed with the same NCA solver; that agreement validates the Bessel-function mapping within NCA, not NCA's accuracy. The exact-solver result cited from Ref. 48 supports the population-inversion mechanism, but not the magnitudes of the cooling, the pairing order parameter, or the extracted beta_eff in the new protocols. If NCA overestimates the pairing susceptibility or the steepness of the distribution function, the effective temperatures, the symmetry-breaking thresholds, and the claimed equivalence to chemically doped states could all be artifacts. The paper is framed as a proof of principles, but the principle is only as solid as the solver used to demonstrate it.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper uses nonequilibrium dynamical mean-field theory (DMFT) with the non-crossing approximation (NCA) as the impurity solver to study the cooling-by-doping mechanism in the single-band Hubbard model. Three demonstrations are presented: (i) photo-doped Mott insulating states with effective inverse temperatures beta_eff ≈ 19, 14, and 13 that show a sharp Drude peak in the optical conductivity, matching that of chemically doped equilibrium systems at the same beta_eff and twice the doping (Fig. 2); (ii) a negative-temperature state in the repulsive Hubbard model that develops a large s-wave superconducting order parameter under a weak applied pair field (Fig. 5); and (iii) a strongly photo-doped Mott insulator that enters an eta-paired state with a large staggered order parameter and a non-decaying induced current (Figs. 6 and 7). The paper is explicitly framed as a proof of principles.","tokens_in":15003,"tokens_out":11890,"duration_ms":115110,"significance":"If the results hold, they are significant for the nonequilibrium DMFT community and for pump-probe and cold-atom experiments: cooling-by-doping is proposed as a way to avoid thermalization bottlenecks and to access cold photo-doped metals, negative-temperature superconductivity, and eta-paired states without coupling to boson baths. The paper is generally well parameterized and contains valuable internal checks, including the AC-quench versus U-quench comparison (Fig. 3), the weak pair-field pulse and persistent-current diagnostics for eta-pairing (Fig. 6), and the use of three doping levels in the conductivity comparison. However, all numerical evidence is generated with a single approximate impurity solver, and several definitional and protocol-level issues need to be resolved before the central claims can be considered established.","major_comments":[{"comment":"The impurity model is solved exclusively with NCA (Sec. II), and all three headline results—the conductivity matching in Fig. 2, the s-wave order parameter in Fig. 5, and the eta-pairing order parameters in Figs. 6 and 7—are produced with this single approximate solver. The only internal cross-check (Sec. III B, Fig. 3) compares an AC-field quench with a U-quench; both calculations use NCA, so it validates the Bessel-function mapping within NCA but not the accuracy of NCA in the low-temperature, symmetry-broken, or negative-temperature regimes that are central here. NCA is uncontrolled in precisely those regimes, and the paper itself relies on an NCA phase diagram (Ref. 50) to locate beta_c. I request a benchmark of at least one of the three protocols against a numerically exact or independent impurity solver in the relevant parameter regime, together with a statement of the expected NCA error. Without such a check, the reported effective temperatures and order parameters could be solver artifacts.","section":"Sec. II, Figs. 2, 5-7"},{"comment":"The method section states that the narrow bands have the same temperature as the initial equilibrium system, but in all simulations the band edges are specified as Fermi-function cutoffs with temperature 0.01–0.05, whereas the initial system is at beta = 5 (T = 0.2). The reservoirs used in the calculations are therefore substantially colder than the initial system, which could provide a trivial cooling channel. Please clarify whether the cutoff temperature is a physical temperature or a numerical broadening; if it is physical, reconcile it with the 'same temperature' statement and test the cooling effect with bands at the same temperature as the initial state (or in the closed setup of Ref. 40). Otherwise the claim that the bandwidth, rather than the temperature, drives the cooling is not supported by the presented simulations.","section":"Sec. II vs. Secs. III A-C"},{"comment":"The effective temperature beta_eff is extracted from a Fermi-function fit to A</A in the energy range of the upper Hubbard band, but the headline comparison is the low-frequency Drude conductivity, which is controlled by states near the chemical potential. Because the distribution functions are not exactly Fermi-like (see Fig. 5, right panel), the value of beta_eff may depend on the chosen fit window. Please show the robustness of beta_eff to the fit range (e.g., fitting the lower Hubbard band or both bands), report the fit residuals, and, if the two bands give different beta_eff, qualify the equivalence statement in the abstract. This point is load-bearing because the central 'same low-frequency conductivity as a chemically doped system with 2x% doping and beta=beta_eff' claim depends on beta_eff being well-defined.","section":"Sec. III A, Fig. 2"},{"comment":"The superconducting demonstration in Fig. 5 is performed with a constant applied pair field of strength 0.001, and the paper uses the heuristic criterion that an order parameter larger than 0.1 indicates spontaneous symmetry breaking. This criterion is reasonable, but it does not by itself exclude a large nonlinear induced response; the equilibrium comparison in Fig. 4 uses the same NCA solver and pair-field values, so it cannot serve as an independent calibration. Unlike the eta-pairing case in Sec. III C (dashed line in Fig. 6), no simulation is shown in which the pair field is switched off after the order has formed and the order parameter persists. Please add such a zero-field persistence check (or a divergent zero-field pair susceptibility) to support the claim of spontaneous s-wave superconductivity in the negative-temperature state.","section":"Sec. III B, Fig. 5"}],"minor_comments":[{"comment":"There are two typos: 'superconductvity' in Sec. III B and 'oder parameter' in the Fig. 7 caption.","section":"Sec. III B; Fig. 7 caption"},{"comment":"The full pulse protocol for the superconducting simulation is not specified: the text says the frequency is 'continuously lowered' but does not give Omega(t) or fenvelope(t), unlike the eta-pairing section which provides Eq. (14). Please provide the complete pulse parameters for reproducibility.","section":"Sec. III B"},{"comment":"The caption says 'grey (blue) dashed lines' but the text distinguishes gray and blue equilibrium curves; please clarify which color corresponds to x% and 2x% doping in both the spectral and conductivity panels.","section":"Fig. 2"},{"comment":"The statement that 'the noninteracting narrow bands have the same temperature as the initial equilibrium system' should be corrected or qualified in view of the cutoff temperatures used in the simulations.","section":"Sec. II"},{"comment":"Ref. 54 is cited as 'in preparation'; if a published version exists, please update the reference.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is from a strong group and the results are interesting, but the NCA-only evidence is a real risk for a paper with such broad claims. The authors should be able to add at least one exact-solver benchmark and the zero-field SC persistence check; if those are provided, the paper would be suitable for publication. The temperature inconsistency of the narrow bands also needs clarification before acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper delivers on its title—three genuinely new demonstrations of cooling-by-doping in DMFT—and it is written by people who know the pitfalls. The one thing to keep in mind is that every impurity solution uses NCA, and the central order parameters and effective temperatures are not cross-checked against an exact solver. That is a real soft spot, not a dealbreaker.\n\nWhat is new: (1) the photo-doped Mott conductivity matches a chemically doped system at twice the doping and the same beta_eff; (2) a cold negative-temperature s-wave superconductor prepared by doping the repulsive Hubbard model; (3) an eta-paired state with a nondecaying current in a large-gap Mott insulator. The first of these is a clean, falsifiable statement within the model. The second and third are the kind of states people have speculated about but not actually prepared in DMFT.\n\nThe paper does several things right. The method section gives explicit parameters (U, beta, pulse shapes, band widths), so the simulations are reproducible in principle. The AC-quench versus U-quench comparison in Sec. III B is a sensible internal check. The eta-pairing section includes a pair-field pulse without a constant field to argue for spontaneous symmetry breaking, and measures the induced current. That is more than many proof-of-principle papers do.\n\nThe soft spots are proportional. NCA is uncontrolled near a Fermi-liquid or superconducting instability, and the magnitudes of beta_eff and the order parameters could shift with a better solver. The cited exact-solver result in Ref. 48 supports the population inversion mechanism but not the new protocol's cooling efficiency or pairing amplitudes. Also, the phase diagram for eta-pairing is deferred to an in-preparation paper (Ref. 54), which means part of the interpretation is not independently checkable yet. The effective temperatures are fitted without error bars. None of this changes the qualitative picture, but it does mean the quantitative claims should be read as NCA-level estimates.\n\nI would send this to peer review without hesitation. It is a serious computational paper with novel results, and the NCA concern is exactly what referees can push on. If a referee asks for one exact-solver cross-check for one of the three protocols, that is a reasonable request and likely achievable. My own verdict would be 'accept after reasonable revision.'","headline":"Solid proof-of-principle paper: three new nonequilibrium states prepared by cooling-by-doping in DMFT, but the NCA-only impurity solver leaves the quantitative results without a cross-check.","tokens_in":15548,"tokens_out":2834,"would_cite":true,"duration_ms":28985,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Transiently coupling a Hubbard model to narrow full and empty bands removes enough entropy to create cold photo-doped Mott states, a negative-temperature s-wave superconductor, and an eta-paired state.","keywords":["cooling by doping","Hubbard model","nonequilibrium dynamical mean-field theory","Mott insulator","optical conductivity","negative temperature superconductivity","eta pairing","photo-doping"],"falsifier":"Rerun the two decisive simulations, the negative-temperature s-wave superconductor at $U=2.52$ and the eta-paired state at $U=9$, with an impurity solver that does not use the non-crossing approximation, for example a continuous-time quantum Monte Carlo solver or exact diagonalization on a finite cluster, and check whether the order parameters still grow to the reported magnitudes and whether the extracted $\\beta_{\\mathrm{eff}}$ values remain below the thresholds for symmetry breaking. If they do not, the demonstrations are artifacts of the approximate solver.","tokens_in":14449,"feed_emoji":"🧊","tokens_out":12512,"duration_ms":121406,"temperature":0.7,"pith_summary":"This paper aims to establish that cooling-by-doping, transiently coupling a Hubbard model to two narrow bands, one full and one empty, can prepare genuinely cold nonequilibrium states of the repulsive Hubbard model without an external heat bath. Using nonequilibrium dynamical mean-field theory, the authors report three concrete demonstrations: a photo-doped Mott insulator whose low-frequency optical conductivity matches that of a chemically doped system at twice the photo-doping concentration, a negative-temperature state that becomes an s-wave superconductor, and an eta-paired superconducting state in a strongly photo-doped Mott insulator. The cooling works because the narrow bands absorb entropy while the pulse moves electrons into the upper Hubbard band and out of the lower one. If correct, the result matters because it provides an experimentally plausible route around the heating and slow relaxation bottlenecks that have blocked cold photo-doped states in earlier simulations.","feed_headline":"Cooling by doping yields superconductivity in repulsive Hubbard model","feed_subtitle":"Moving entropy into flat bands makes cold Mott states that host s-wave and eta-paired superconductivity","key_machinery":"The load-bearing mechanism is the cooling-by-doping protocol: a chirped hopping pulse of the form $v_{\\mathrm{system\\text{-}bath}}(t)=a_{\\max} f_{\\mathrm{envelope}}(t)\\sin(\\Omega(t)t)$ couples the system to a narrow full band and a narrow empty band, transferring electrons into the upper Hubbard band and out of the lower Hubbard band while the narrow bands carry away entropy. The particle-hole symmetric arrangement of the two bands keeps the chemical potential fixed, which the paper argues is important for superconductivity. The quantitative engine is nonequilibrium dynamical mean-field theory on the infinite-connected Bethe lattice, solved with the non-crossing approximation; Nambu matrix self-consistency equations detect s-wave pairing, and a sign-flipped version detects $\\eta$-pairing, defined as staggered s-wave pairing with opposite phase on the two sublattices. The paper's central quantitative identity is the equivalence between a photo-doped state with $x\\%$ doublons and $x\\%$ holons and an equilibrium chemical doping of $2x\\%$ at the same effective inverse temperature $\\beta_{\\mathrm{eff}}$, with $\\beta_{\\mathrm{eff}}$ extracted from Fermi-function fits to the occupation ratio $A^<(\\omega)/A(\\omega)$.","core_discovery":"On the paper's own terms, the central discovery is that entropy can be reshuffled out of a Hubbard system into narrow full and empty bands faster than the system heats itself, so the remaining population of doublons and holons is characterized by a low effective temperature. In the Mott regime ($U=9$) the resulting photo-doped states have inverse effective temperatures $\\beta_{\\mathrm{eff}}\\approx 13$-$20$ and sharp quasiparticle peaks, and their low-frequency conductivity is, within DMFT, identical to that of a chemically doped equilibrium state with the same $\\beta_{\\mathrm{eff}}$ and $2x\\%$ doping when the photo-doped state has $x\\%$ doublons and $x\\%$ holons. In the metallic regime ($U=2.52$) the same protocol generates a population-inverted negative-temperature state; after the narrow bands are decoupled it thermalizes to $\\beta=-7.3$ and develops an s-wave superconducting order parameter of magnitude about 0.36, which the paper identifies with the equilibrium superconducting state of the attractive Hubbard model. In the strongly interacting regime ($U=9$) with large doublon and holon density, the protocol induces an $\\eta$-paired staggered superconducting state with a nonzero order parameter and a persistent current, stable well beyond the simulation window. The paper presents all three as proofs of principle that cooling-by-doping can reach states that direct photodoping or boson-bath cooling could not.","pith_inferences":["The paper's open-system setup treats the narrow bands as equilibrium entropy sinks that never heat up; a closed-system version would presumably cool less, so a natural extension is to quantify how much entropy a finite-width narrow band can absorb before its own temperature rises.","Because the low-frequency equivalence with chemical doping is stated to hold within DMFT, an immediate test is whether the same conductivity matching survives in non-DMFT methods such as cluster or diagrammatic approaches; if it does, the effective-doping correspondence may be a general property of photo-doped Mott insulators.","The same entropy-reshuffling idea could be applied to magnetic order: coupling to narrow bands that selectively accept entropy from one spin species or one sublattice might prepare cold antiferromagnetic states, which the current paper does not simulate.","A practical diagnostic suggested by the paper's logic is that a sharp Drude peak appearing after resonant excitation into a narrow band is a signature of effective temperatures far below the nominal lattice temperature; pump-probe experiments could look for this crossover as the chirp frequency is tuned."],"forward_implications":["Photo-doped Mott insulators should show a sharp Drude peak and quasiparticle features when the doping is done through narrow bands, in contrast to the broad bad-metal response seen after ordinary photodoping.","For a photo-doped state with $x\\%$ doublons and $x\\%$ holons, comparisons with equilibrium should use $2x\\%$ chemical doping at the same $\\beta_{\\mathrm{eff}}$, not $x\\%$.","A repulsively interacting Hubbard model can host conventional s-wave superconductivity in a cold negative-temperature state, with the same properties as the attractive-Hubbard superconductor at positive temperature.","Eta-paired superconducting states can be realized in large-gap Mott insulators with high doublon and holon densities and are long-lived because the recombination time grows exponentially with the gap; their positive effective temperature makes them robust against phonon or positive-temperature bath coupling.","Cooling-by-doping bypasses the thermalization bottleneck observed in boson-bath cooling protocols by moving the system along the filling axis instead of waiting for quasiparticle formation."],"supporting_citations":[{"why":"Introduces the cooling-by-doping effect from narrow bands that the paper exploits as its preparation tool.","marker":"[40]"},{"why":"Provides the nonequilibrium dynamical mean-field theory formalism used for all simulations.","marker":"[41]"},{"why":"Supplies the non-crossing approximation impurity solver used to close the DMFT equations.","marker":"[44,45]"},{"why":"Documents the bad-metal behavior and quasiparticle bottleneck in photo-doped Mott insulators that cooling-by-doping is designed to overcome.","marker":"[34]"},{"why":"Establishes the AC-field negative-temperature population inversion and effective attractive interaction used in the s-wave superconductivity section.","marker":"[48]"},{"why":"Defines eta-pairing, the staggered pairing order the paper induces in the Mott regime.","marker":"[47]"},{"why":"Provides the NCA phase diagram for the attractive Hubbard model, including the critical inverse temperature used to interpret the superconducting susceptibility.","marker":"[50]"},{"why":"Earlier exact-diagonalization evidence for photo-enhanced eta-pairing correlations that the present work extends to symmetry breaking in the thermodynamic limit.","marker":"[53]"},{"why":"Establishes the exponential growth of doublon-holon lifetime with the gap and the entropy of photo-doped Mott states, supporting the longevity of the eta-paired state.","marker":"[15]"}],"fun_headline_variants":["Entropy reshuffling cools Hubbard model to superconducting states","Doping-induced cooling creates superfluid from repulsive Hubbard","Entropy dump into flat bands yields eta-paired supercurrents","Cooling by doping makes negative temperature and s-wave pairing","Entropy-cooled Hubbard states: from Drude peak to eta pairing"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The approximate impurity solver used in every dynamical mean-field simulation is quantitatively trustworthy for the broken-symmetry and negative-temperature states, so the reported order parameters and effective temperatures are not solver artifacts.","fun_headline_variants_meta":{"raw":{"variants":["Entropy reshuffling cools Hubbard model to superconducting states","Doping-induced cooling creates superfluid from repulsive Hubbard","Entropy dump into flat bands yields eta-paired supercurrents","Cooling by doping makes negative temperature and s-wave pairing","Entropy-cooled Hubbard states: from Drude peak to eta pairing"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000847,"raw_usage":{"total_tokens":3692,"prompt_tokens":958,"completion_tokens":2734,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":574,"completion_tokens_details":{"reasoning_tokens":2648}},"tokens_in":574,"tokens_out":2734,"duration_ms":20997,"temperature":1.0,"reasoning_tokens":2648,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:38:56.555211+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Rerun the two decisive simulations, the negative-temperature s-wave superconductor at $U=2.52$ and the eta-paired state at $U=9$, with an impurity solver that does not use the non-crossing approximation, for example a continuous-time quantum Monte Carlo solver or exact diagonalization on a finite cluster, and check whether the order parameters still grow to the reported magnitudes and whether the extracted $\\beta_{\\mathrm{eff}}$ values remain below the thresholds for symmetry breaking. If they do not, the demonstrations are artifacts of the approximate solver.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the nonequilibrium dynamical mean-field theory formalism used for all simulations."},{"cited_title":"Eckstein and P","cited_arxiv_id":null,"evidence_quote":"Documents the bad-metal behavior and quasiparticle bottleneck in photo-doped Mott insulators that cooling-by-doping is designed to overcome."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines eta-pairing, the staggered pairing order the paper induces in the Mott regime."},{"cited_title":"Kaneko, T","cited_arxiv_id":null,"evidence_quote":"Earlier exact-diagonalization evidence for photo-enhanced eta-pairing correlations that the present work extends to symmetry breaking in the thermodynamic limit."},{"cited_title":"Eckstein and P","cited_arxiv_id":null,"evidence_quote":"Establishes the exponential growth of doublon-holon lifetime with the gap and the entropy of photo-doped Mott states, supporting the longevity of the eta-paired state."}],"review_version":1}