{"id":"acf2f1d9-503c-4c51-8447-545e11d130fd","arxiv_id":"2507.21804","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Interacting fermions with local dephasing, solved via DMFT and a quantum Boltzmann equation, heat to infinite temperature with a prethermal plateau at weak dephasing, and the unitary thermalization front is destroyed by irreversibility.","lead":"This paper studies how interacting electrons in a lattice heat up when coupled to a local dephasing bath, using a large-connectivity mean-field approach. It finds that the system heats to infinite temperature with interaction-dependent rates, and that the ballistic thermalization front seen in closed systems bends and disappears under dissipation.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The QBE separation-of-timescales assumption is untested for U/th=2 at gamma/th up to 2, so the interaction-dependent heating rates and the bending/disappearing thermalization front may be solver artifacts.","rationale":"The paper's unique quantitative content is the interaction-dependent heating rate, the prethermal plateau, and the modification of the thermalization front. Each of these is computed with the QBE solver, whose stated validity condition is untested for the interacting case at strong dephasing. The reader's weakest-assumption analysis identified exactly this point, and my reading agrees. The manuscript does give independent support in the U=0 limit, where an exact analytical solution exists, but that does not cover the interacting QBE update. A direct comparison with full Noneq-DMFT for moderate gamma would be the cleanest settlement: the authors already have the impurity solver machinery, and finite t_max runs are expensive but feasible. If the benchmark passes, the central claims are credible; if it fails, the rates and front interpretation need substantial qualification, though the infinite-temperature endpoint itself would remain correct by construction. I therefore see no reason to move the reader's conditional verdict, and no reason to manufacture a stronger objection.","tokens_in":21326,"tokens_out":4314,"duration_ms":61274,"concrete_test":"Benchmark the QBE against full Noneq-DMFT (Kadanoff-Baym equations with the same IPT impurity solver and dissipative self-energy) for U/th = 2, initial beta = 20, for gamma/th = 0.1, 0.5, and 2.0, including the photoexcitation case Gamma/th = 1 used for the front analysis, propagating to t_max ~ 20-30 with sufficiently fine time steps to resolve memory integrals. Compare beta_eff(t), kinetic and potential energy, and F(omega, t). If the maximum relative deviation in beta_eff(t) exceeds about 10% at any time for gamma/th >= 0.5, the separation-of-timescales assumption is violated and the reported interaction-dependent rates and front modification are not established; if agreement is within tolerance, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative results are produced entirely by the non-perturbative QBE solver of Sec. III.B, whose stated validity condition is a separation of time scales: \"the time evolution of the system has to be slow with respect to relevant internal energy differences... such as the linewidth or relevant spectral features.\" For gamma/th = 2.0, the dephasing-induced linewidth is comparable to the single-particle bandwidth, so this condition is not met. Nevertheless, Figs. 2-3 report interaction-dependent relaxation rates and prethermal plateaus precisely in this regime. The U=0 case is solved analytically in Appendix C, but that validates only the non-interacting dissipative self-energy, not the QBE update of the distribution function for U=2. The same QBE solver is used in the step-by-step DMFT construction of Sec. VI, so the claimed bending and disappearance of the thermalization front shares the same vulnerability. The infinite-temperature endpoint is not at stake because rho = 1 is an exact steady state of the Lindbladian; what is at stake is the rates, plateau lifetimes, and front shape, which are the paper's new claims.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies the heating dynamics of the half-filled Fermi-Hubbard model on a Bethe lattice in the presence of local dephasing, using an extension of nonequilibrium DMFT to Markovian open systems. The impurity problem is solved with a non-perturbative quantum Boltzmann equation (QBE) in which the distribution function F(ω,t) is evolved while the retarded self-energies and spectra are obtained from a nonequilibrium steady-state impurity loop. Two protocols are considered: a sudden quench of the dephasing rate γ and a simultaneous photoexcitation with amplitude Γ and dephasing quench. The central claims are that the system heats to an infinite-temperature steady state with an interaction-dependent relaxation rate; that weak dephasing produces a long-lived prethermal plateau with a nonthermal distribution and a quasiparticle-like spectrum; and that, in the step-by-step DMFT construction of Sec. VI, dephasing bends, flattens, and eventually destroys the ballistic thermalization front found for closed systems. The infinite-temperature endpoint is an exact fixed point of the dephasing Lindbladian, so the paper's nontrivial content lies in the rates, transients, spectra, and front morphology.","tokens_in":21486,"tokens_out":7954,"duration_ms":89531,"significance":"If the quantitative claims are reliable, the paper is a useful contribution to open-system DMFT and to the phenomenology of dissipative heating in correlated fermions. It is methodologically transparent, uses no fitted parameters, provides an exact analytical solution for the U=0 dissipative case in Appendix C, and employs an exact resummation for the local dephasing self-energy [38,49]. The main significance hinges on whether the QBE approximation remains valid for the dephasing rates and interaction strengths at which the headline results are reported; that point is investigated in the major comments. Disagreement with the closed-system thermalization picture is not by itself a concern: the mechanism is clearly stated (the fixed point of the Lindbladian and the loss of initial-condition memory), and the qualitative disappearance of the front at strong dephasing is a robust expectation even if the precise shape is approximate.","major_comments":[{"comment":"The QBE solver used for all interacting results assumes a separation of timescales: the time evolution must be slow compared with relevant linewidths and spectral features. For γ/th up to 2.0, the dephasing-induced linewidth is comparable to the single-particle bandwidth, so the stated condition is not met, yet Figs. 2(b,c), 3(b), 5, and 6 report interaction-dependent relaxation rates, prethermal plateau lifetimes, and front shapes in this regime. The U=0 analytical solution in Appendix C validates only the noninteracting dissipative self-energy, not the QBE update of F(ω,t) at U=2. I request a benchmark of the QBE against the full Noneq-DMFT equations for representative parameters (for example γ/th = 0.1, 0.5, 2.0 at U/th = 2), or, if such a calculation is too costly, a clear restriction of the quantitative claims to γ much smaller than the bandwidth and a qualitative-only interpretation of the strong-dephasing data.","section":"Sec. III.B, Figs. 2-3 and 5-6"},{"comment":"The impurity solver combines second-order IPT for the Hubbard interaction, Eq. (14), with the exact/resummed dephasing self-energy, Eq. (15). The abstract describes the method as weak-coupling perturbation theory in interaction and dephasing; however, for U/th = 2 and γ/th = 2 the self-consistent IPT is not a controlled expansion. Since the interaction-dependent heating rates in Figs. 2-3 and the prethermal spectra in Fig. 4 are derived from this approximation, the paper should provide at least one benchmark against an exact impurity solver for the dissipative Anderson model (the Diagrammatic Monte Carlo of Refs. [38,39] is natural) and a statement of the expected truncation error. Without such a check, the U-dependence of the relaxation rate is difficult to separate from solver artifacts.","section":"Secs. III.A, IV, V"},{"comment":"The central claim of Sec. VI, that the thermalization front 'bends and flatten out' and disappears with increasing γ, is supported only by visual inspection of the β_eff,n(t) panels. The manuscript does not define the front position, its sharpness, or a front velocity, and the γ=0.001 behavior (decrease, minimum, then return to near-initial temperature) is not obviously the same object as the ballistic front of the unitary case studied in Ref. [40]. I ask for a quantitative diagnostic—for example a level contour of β_eff,n in the (n,t) plane, the extracted front velocity, and a width—applied uniformly to the unitary and dissipative data.","section":"Sec. VI, Fig. 6"}],"minor_comments":[{"comment":"The definition of β_eff(t) from F(ω,t) ∼ −β_eff ω/4 around ω=0 is not accompanied by the fitting interval or an error estimate; please specify the frequency window and tolerance used in Figs. 3, 5, and 6.","section":"Sec. IV.B"},{"comment":"There are several typos: 'self-consisitent' in Sec. III.A, 'irriversibility' in Sec. VI, and 'it's seem' in Appendix C; also Eq. (13) lacks the spin subscript on the left-hand side.","section":"Various"},{"comment":"References [13] and [49] are the same work (T. Jin et al.) and should be consolidated.","section":"References"},{"comment":"The color scale appears logarithmic but the color-bar labels are not explained; please add a caption note describing the scale and the meaning of the numerical labels.","section":"Figs. 4 and 7"},{"comment":"The caption mentions 'the gray dot represents the non-dissipative case' but the caption of panels (d-f) does not identify which curve is the gray dot; please clarify.","section":"Fig. 5"},{"comment":"The sentence 'where βi and βf are the initial and final inverse temperatures of the full-DMFT solution, shown in the top panels of Fig. 6' would be clearer if βf were marked explicitly in those panels.","section":"Sec. VI"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely acceptable after the requested benchmark. I would prioritize the QBE/Noneq-DMFT comparison over the IPT validation; if the benchmark is impossible, the strong-dephasing results should be downgraded to qualitative. The front-extraction diagnostic is also needed for the Sec. VI claim to be assessable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a serious, well-written paper that makes a plausible case that dephasing drives the Fermi-Hubbard model to infinite temperature with interaction-dependent rates, and that dissipation destroys the unitary thermalization front. The endpoint itself is built into the model—rho=1 is an exact steady state of the Lindbladian—so the real content is in the rates, the prethermal plateau, and the front analysis. Those are new, and the DMFT+QBE machinery is a sensible way to access them.\n\nWhat the paper does well: it gives a clean derivation of the DMFT embedding for Markovian dephasing, resums the dissipative self-energy exactly, provides an exact analytic solution for U=0 as a benchmark, and presents a coherent physical picture of the prethermal state. The step-by-step DMFT analysis that reveals the front bending is a nice extension of the authors' earlier unitary result, and the interpretation—dephasing erases memory of the initial condition, so the front flattens—is physically reasonable.\n\nThe soft spots are real but not fatal. The main one: the QBE relies on a separation of timescales, and for gamma/th up to 2 the dephasing linewidth is comparable to the bandwidth, so the approximation is outside its stated regime. The U=0 analytic solution validates the dissipative self-energy but not the QBE update for U=2, and no benchmark against full Noneq-DMFT is provided for the interacting case. So the quantitative rates and plateau lifetimes at the larger gamma values should be treated with caution. The front analysis in Sec. VI is built on the same QBE solver and inherits this concern, though the qualitative conclusion is probably robust. A second, lesser issue: the step-by-step DMFT uses the iteration index n as a proxy for bath adaptation, and the physical meaning of that front is not fully pinned down. Also, no code or data is provided, which makes independent verification harder.\n\nOverall, the central narrative holds up, but the paper should be asked to benchmark QBE against exact or alternative solvers at least for one or two moderate gamma values, and to be more explicit about where the QBE is trusted. It deserves a serious referee, and it would be a useful read for people working on open-system DMFT and quantum simulators. I'd probably cite it if I worked in that area.","headline":"Solid DMFT+QBE study of dephasing-induced heating in the Hubbard model; the main new claims are plausible but the QBE validity at the strongest dephasing rates is unchecked.","tokens_in":694,"tokens_out":937,"would_cite":true,"duration_ms":56582,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Dephasing drives interacting Hubbard fermions to infinite temperature, with interactions controlling the heating rate and erasing the ballistic thermalization front.","keywords":["dissipative Fermi-Hubbard model","local dephasing","infinite-temperature thermalization","nonequilibrium DMFT","quantum Boltzmann equation","prethermal plateau","thermalization front","dissipative quantum impurity model"],"falsifier":"Run the full nonequilibrium DMFT (Kadanoff-Baym) evolution for $U/t_h=2$ at $\\gamma/t_h=0.001$ and $\\gamma/t_h=2$, and compare the effective temperature $\\beta_{\\rm eff}(t)$ with the quantum-Boltzmann result; disagreement beyond the stated numerical tolerance, or failure of $\\beta_{\\rm eff}$ to relax to zero with a flat distribution, would falsify the central claim. A cheaper check is the predicted prethermal plateau: at $\\gamma/t_h=0.01$ and $U/t_h=2$, $\\beta_{\\rm eff}$ must remain nearly constant for the time window shown before resuming its decay.","tokens_in":21054,"feed_emoji":"🔥","tokens_out":9321,"duration_ms":92903,"temperature":0.7,"pith_summary":"The paper sets out to show that a dissipative Fermi-Hubbard model with local dephasing heats toward a featureless infinite-temperature steady state, and that interactions strongly control how fast it gets there. Working in the infinite-coordination limit through nonequilibrium dynamical mean-field theory, the authors solve the self-consistent impurity problem with weak-coupling perturbation theory and a quantum Boltzmann equation. They find a prethermal plateau at weak dephasing, where a coherent quasiparticle peak survives and the distribution function is non-thermal at high frequencies, followed by exponential relaxation to infinite temperature. They also show that the ballistic thermalization front of the closed Hubbard model bends, flattens, and eventually disappears as dephasing increases, because the open dynamics no longer retains memory of the initial condition.","feed_headline":"Dephasing bends and erases the Hubbard thermalization front","feed_subtitle":"Interactions slow heating into a prethermal plateau until dissipation takes over and wipes out memory of the initial state.","key_machinery":"The load-bearing object is the self-consistent impurity problem of nonequilibrium DMFT for Markovian fermions, in which the infinite-coordination Bethe lattice maps exactly to a dissipative Anderson impurity with local dephasing and hybridization $\\Delta_\\sigma(t,t') = t_h^2 G_\\sigma(t,t')$. The dynamics is carried by a quantum Boltzmann equation for the energy distribution $F(\\omega,t)$, whose scattering integral is evaluated at each time step by solving a nonequilibrium steady-state impurity model with the dissipative self-energy $\\Sigma_\\gamma(t,t') = \\gamma G(t,t)\\,\\delta(t-t')$; this dissipative self-energy is exact for local dephasing, while the Hubbard interaction is treated by iterated perturbation theory. A second key mechanism is the step-by-step DMFT iteration that exchanges the long-time and self-consistency limits, which exposes the thermalization front as a travelling wave in the $(n,t)$ plane.","core_discovery":"The central discovery is that switching on local dephasing $\\gamma$ in the half-filled Fermi-Hubbard model on a Bethe lattice produces irreversible heating to the maximally mixed state $\\rho_\\infty \\propto \\mathbb{1}$, with a relaxation rate that depends strongly on both $U$ and $\\gamma$. For $U/t_h = 2$ and weak dephasing the effective inverse temperature $\\beta_{\\rm eff}$ initially drops quickly, then stabilizes in a long-lived prethermal plateau, then decays to zero; the crossover time $t^*$ scales roughly as $1/\\gamma$ and is nearly independent of $U$. The steady-state spectral function is not trivial: a coherent quasiparticle peak survives weak dephasing and melts as $\\gamma$ increases, leaving only broad Hubbard bands, while the distribution becomes flat in frequency. Looking at the DMFT self-consistency iteration by iteration, the paper shows that the sharp linearly dispersing thermalization front of the unitary case persists only for very weak dephasing; at larger $\\gamma$ each iteration settles into a nonequilibrium steady state at a temperature between initial and final, so the front bends and flattens and ultimately disappears.","pith_inferences":["Not stated in the paper, but a direct corollary of the energy-insensitive action of dephasing: for $\\gamma \\gg t_h$ the heating rate should become essentially independent of $U$, and this could be tested by measuring $\\beta_{\\rm eff}(t)$ over a range of interaction strengths.","The paper does not discuss the cold-atom readout, but in Hubbard simulators where intensity noise or spontaneous emission acts as a local dephasing bath, the prethermal plateau should appear as a slow drift of the measured momentum distribution after the noise is switched on, with a plateau lifetime that grows with $U$.","One diagnostic suggested by the erased front is that a dissipative many-body system can be distinguished from a closed one by the absence of a light-cone-like travelling wave in a self-consistency or correlation-spreading measurement, because the bath forgets the initial condition faster than it adapts."],"forward_implications":["For weak dephasing, $\\gamma/t_h \\lesssim 0.025$ at $U/t_h=2$, the system forms a long-lived prethermal plateau in $\\beta_{\\rm eff}$ while the total energy keeps drifting, so effective temperature and energy decouple on intermediate times.","At strong dephasing the coherent quasiparticle peak in the spectral function is destroyed and the distribution function flattens across all frequencies, signalling the true infinite-temperature state.","A photoexcitation pulse whose amplitude is comparable to or larger than $\\gamma$ stabilizes the prethermal plateau and slows the subsequent heating.","In the DMFT iteration picture, increasing $\\gamma$ from $0.001$ to $0.6$ bends and flattens the linear thermalization front, and for the largest rates the front disappears entirely.","For noninteracting fermions, the kinetic energy rises exponentially to zero and $\\beta_{\\rm eff}$ vanishes exponentially with a rate set by $\\gamma$."],"supporting_citations":[{"why":"supplies the nonequilibrium DMFT mapping for Markovian open quantum systems that underlies the whole calculation.","marker":"[37]"},{"why":"provides the dissipative Anderson impurity model and the exact resummation used for the local dephasing self-energy.","marker":"[38]"},{"why":"defines the unitary thermalization front that the paper shows is bent and erased by dephasing.","marker":"[40]"},{"why":"supplies the quantum Boltzmann equation used to propagate the distribution function with linear time cost.","marker":"[45]"},{"why":"gives the DMFT self-consistency relation $\\Delta(t,t')=t_h^2 G(t,t')$ for the Bethe lattice, used throughout.","marker":"[35]"},{"why":"supports the closed form of the dissipative self-energy via the exact quantum-resistor description of dephasing.","marker":"[49]"}],"fun_headline_variants":["Dephasing erases the Hubbard thermalization front","Prethermal plateau, then irreversible heating to infinite T","Dephasing melts quasiparticle peak and flattens thermalization front","Interactions slow heating; dephasing wipes out initial-state memory","Open-system fermions heat irreversibly to infinite temperature"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method assumes a separation of timescales: the heating must be slow enough that, at each moment, the system can be treated as a nonequilibrium steady state with the current distribution function, and this assumption is not benchmarked against the full nonequilibrium DMFT solution for the interacting case, especially at dephasing rates up to $\\gamma/t_h = 2$ where $\\gamma$ is comparable to the bandwidth.","fun_headline_variants_meta":{"raw":{"variants":["Dephasing erases the Hubbard thermalization front","Prethermal plateau, then irreversible heating to infinite T","Dephasing melts quasiparticle peak and flattens thermalization front","Interactions slow heating; dephasing wipes out initial-state memory","Open-system fermions heat irreversibly to infinite temperature"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001114,"raw_usage":{"total_tokens":4649,"prompt_tokens":965,"completion_tokens":3684,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":581,"completion_tokens_details":{"reasoning_tokens":3598}},"tokens_in":581,"tokens_out":3684,"duration_ms":35654,"temperature":1.0,"reasoning_tokens":3598,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T12:22:27.897817+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the full nonequilibrium DMFT (Kadanoff-Baym) evolution for $U/t_h=2$ at $\\gamma/t_h=0.001$ and $\\gamma/t_h=2$, and compare the effective temperature $\\beta_{\\rm eff}(t)$ with the quantum-Boltzmann result; disagreement beyond the stated numerical tolerance, or failure of $\\beta_{\\rm eff}$ to relax to zero with a flat distribution, would falsify the central claim. A cheaper check is the predicted prethermal plateau: at $\\gamma/t_h=0.01$ and $U/t_h=2$, $\\beta_{\\rm eff}$ must remain nearly constant for the time window shown before resuming its decay.","supporting_citations":[{"cited_title":"Pichler, A","cited_arxiv_id":null,"evidence_quote":"supplies the nonequilibrium DMFT mapping for Markovian open quantum systems that underlies the whole calculation."},{"cited_title":"Sarkar, S","cited_arxiv_id":null,"evidence_quote":"provides the dissipative Anderson impurity model and the exact resummation used for the local dephasing self-energy."},{"cited_title":"Poletti, J.-S","cited_arxiv_id":null,"evidence_quote":"defines the unitary thermalization front that the paper shows is bent and erased by dephasing."},{"cited_title":"Buchhold and S","cited_arxiv_id":null,"evidence_quote":"supplies the quantum Boltzmann equation used to propagate the distribution function with linear time cost."},{"cited_title":"Marché, G","cited_arxiv_id":null,"evidence_quote":"gives the DMFT self-consistency relation $\\Delta(t,t')=t_h^2 G(t,t')$ for the Bethe lattice, used throughout."},{"cited_title":"Bernier, D","cited_arxiv_id":null,"evidence_quote":"supports the closed form of the dissipative self-energy via the exact quantum-resistor description of dephasing."}],"review_version":1}