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REVIEW 3 major objections 6 minor 1 cited by

Heating Dynamics of Correlated Fermions under Dephasing

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Dephasing drives interacting Hubbard fermions to infinite temperature, with interactions controlling the heating rate and erasing the ballistic thermalization front.

desk verdict 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. read the letter →

arxiv 2507.21804 v1 pith:GJY2WEAN submitted 2025-07-29 cond-mat.str-el quant-ph

Antonio Picano , Matthieu Vanhoecke , Marco Schirò This is my paper · ORCID
classification cond-mat.str-elquant-ph
keywords dissipativeFermi-Hubbardmodellocaldephasinginfinite-temperaturethermalizationnonequilibriumDMFTquantumBoltzmannequationprethermalplateaufrontimpurity
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 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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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 $\gamma$.

Reading between the lines

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

  • 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.
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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

3 major / 6 minor

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.

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 (3)
  1. [Sec. III.B, Figs. 2-3 and 5-6] 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.
  2. [Secs. III.A, IV, V] 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.
  3. [Sec. VI, Fig. 6] 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.
minor comments (6)
  1. [Sec. IV.B] 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.
  2. [Various] 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.
  3. [References] References [13] and [49] are the same work (T. Jin et al.) and should be consolidated.
  4. [Figs. 4 and 7] 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.
  5. [Fig. 5] 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.
  6. [Sec. VI] 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.

Circularity Check

1 steps flagged · score 2.0 of 10

No by-construction circularity: rates, plateaus, and spectra are computed from stated approximations with no fitted parameters; the only self-citation issue is the authors' own thermalization-front baseline [40], keeping the score at 2.

  1. self citation load bearing [Section VI, 'Emergence of Infinite Temperature Thermalization'; echoed in the Abstract and Conclusions.]
    "In Ref. [40] we have shown that an interacting isolated quantum many-body system, such as the Fermi-Hubbard model, acts as its own thermal bath making local observables reach thermal equilibrium after a nonequilibrium perturbation. ... We now use the same approach for our dissipative Hubbard model with dephasing, namely we solve the DMFT equations step by step following the bath as it adapts to the impurity and viceversa, with the goal of understanding how the DMFT self-consistency allows the lattice model to heat up to infinite temperature."

    The Section VI headline result, that 'the front bends and flatten out' and ultimately disappears, is defined relative to the unitary thermalization front of the authors' own PRL [40], and the step-by-step DMFT construction used to extract beta_eff,n(t) is itself the 'same approach' developed in [40]. The present paper computes the dissipative modification with its own QBE/DMFT solver, so no number reduces by construction to an input; however, the existence, the linearly dispersing edge, and the 'memory of the initial condition' interpretation of the front are imported on the credit of a paper whose author list overlaps with this one (Picano and Schirò). The circularity is therefore framing-level: the baseline against which the new claim is measured is self-cited.

full rationale

The paper's derivation chain is otherwise self-contained. No parameter is fitted: U, gamma, beta_i, and Gamma are model inputs scanned over, and beta_eff is extracted from the computed distribution function rather than imposed. The interaction-dependent heating rates, the prethermal plateau, and the steady-state spectra follow from the stated weak-coupling IPT self-energy plus the dissipative self-energy Sigma_gamma(t,t') = gamma G(t,t) delta(t-t'); the latter is derived in Appendix B, cross-checked against the external result [49], and validated at U=0 by the analytic solution of Appendix C, so the self-cited [38] is not the only support. The QBE solver is taken from [45], which is published with external coauthors Li and Eckstein; the stated separation-of-timescales condition is arguably marginal at gamma/t_h = 2, but that is a correctness or validity risk, not a circular reduction, and accordingly is excluded from this score. The infinite-temperature endpoint is genuinely a property of the chosen dephasing channel (Hermitian jump operators L = sqrt(gamma) n imply that rho_inf = 1 is an exact steady state, as the paper states openly); the computed content is the approach dynamics, namely the rates and transients, which is not by construction. The only circularity-adjacent element is the thermalization-front baseline imported from the authors' own [40], and because the new front modification is computed rather than assumed while [40] itself is independently published with an external coauthor, the score remains at 2 rather than higher.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central claims rest on several domain assumptions from prior work (DMFT exactness, exact dephasing self-energy, QBE separation of timescales, IPT accuracy) plus an interpretive assumption specific to this paper (the physical meaning of finite DMFT iterations). No free parameters are fitted to data and no entities are invented.

assumptions (5)
  • domain assumption The infinite coordination limit (z->infinity) makes DMFT exact for the Bethe lattice, so the lattice problem maps onto a self-consistent impurity problem.
    Standard DMFT; invoked in Sec. III to justify the mapping from the lattice to the impurity model.
  • domain assumption The dissipative self-energy is exactly Sigma_gamma(t,t') = gamma G(t,t) delta(t-t') for local dephasing, as resummed in Refs. [38,49].
    The paper states the resummation result in Appendix B and cites [38,49]; the full proof is not reproduced.
  • domain assumption The QBE approximation assumes the time evolution is slow compared to internal energy differences (linewidths), so a NESS impurity solution applies at each time step.
    Stated in Sec. III.B; this is the central approximation that makes the calculation tractable and is not benchmarked against full Noneq-DMFT.
  • domain assumption IPT (second-order iterated perturbation theory) accurately captures the interaction self-energy for U/th=2 in the dissipative nonequilibrium setting.
    IPT is exact in atomic and non-interacting limits but approximate at finite U; its accuracy here is assumed.
  • ad hoc to paper Finite DMFT iterations n in the step-by-step scheme reveal a physically meaningful thermalization front.
    This interpretive assumption, carried over from the authors' unitary study [40], underpins the claim that dissipation modifies the front.

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Cite this review

Pith. "Pith review of Heating Dynamics of Correlated Fermions under Dephasing." pith.science (2026). https://pith.science/paper/GJY2WEAN

@misc{pith2026250721804,
  author       = {Pith},
  title        = {Pith review of: Heating Dynamics of Correlated Fermions under Dephasing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GJY2WEAN}},
  note         = {Machine review of arXiv:2507.21804}
}
read the original abstract

We study the dissipative dynamics of correlated fermions evolving in presence of a local dephasing bath. To this extent we consider the infinite coordination limit of the corresponding Lindblad master equation, provided by Dynamical Mean-Field Theory for open quantum systems. We solve the resulting quantum impurity problem, describing an Anderson impurity coupled to a local dephasing, using weak-coupling perturbation theory in interaction and dephasing. We show that the dissipative dynamics describes heating towards infinite temperature, with a relaxation rate that depends strongly on interaction. The resulting steady-state spectral functions are however non-trivial and show an interplay between coherent quasiparticle peak and local dephasing. We then discuss how thermalization towards infinite temperature emerges within DMFT, by solving the impurity problem throughout its self-consistency. We show that thermalization under open quantum system dynamics is qualitatively different from the closed system case. In particular, the thermalization front found in the unitary is strongly modified, a signature of the irreversibility of the open system dynamics.

Figures

Figures reproduced from arXiv: 2507.21804 by the authors.

Figure 1
Figure 1. Quench protocol for the dissipative Fermi-Hubbard model — An interacting lattice system, characterized by the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Dissipative Fermi-Hubbard Model - Dynamics of the kinetic and potential energy for increasing values of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Dissipative Fermi-Hubbard Model - Dynamics of the effective temperature [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Dissipative Fermi-Hubbard Model - Spectral prop [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Dissipative Fermi-Hubbard Model under photo-excitation - (a-c) Dynamics of the effective temperature as a function [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Thermalization Front of the Dissipative Hubbard Model for the Effective Temperature - Panel (a-h) describes the [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Dissipative Fermi-Hubbard Model - Spectral prop [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: Emergence of Infinite Temperature Thermalization - Evolution of the steady-state effective temperature in the [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantum algorithm for dephasing of coupled systems: decoupling and IQP duality

    quant-ph 2026-01 conditional novelty 6.0 of 10

    A quantum algorithm simulates unital dephasing dynamics by sampling stochastic unitaries and decouples coupled fermion-boson dephasing into an IQP circuit that controls the fermion evolution.

Reference graph

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    The Weiss impurity Green’s functionG is obtained by incorporating the hybridization of the bath via: G−1 σ (t, t′) = G−1 0,σ(t, t′) − ∆σ(t, t′) , (11) where ∆σ(t, t′) is the hybridization function ob- tained from the previous DMFT iteration or initial guess

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    The full interacting impurity Green’s function Gσ(t, t′) is computed via the Dyson equation: G−1 σ (t, t′) = G−1 σ (t, t′) − Σint,σ(t, t′) , (12) 4 where Σint,σ(t, t′) is the impurity self-energy, in- corporating both coherent (ΣU,σ) and dissipative (Σγ,σ) interaction: Σint(t, t′) ≡ ΣU,σ(t, t′) + Σγ,σ (t, t′) (13) The Hubbard interaction term ΣU,σ is comp...

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    This excitation is mod- eled as a pulse characterized by a durationT0 = 1 and an amplitude Γ, representing the strength of the coupling induced by the pulse

    The updated Green’s functionGσ(t, t′) is then used to compute a new hybridization function via the DMFT self-consistency condition (9), ∆σ(t, t′) = t2 h Gσ(t, t′) + Γ(t, t′) , (16) where we introduced an additional contribution to the hybridization function,Γ(t, t′), in order to sim- ulate a photo-excitation. This excitation is mod- eled as a pulse charac...

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    (21) in order to determine ¯A(ω) = − 1 π ℑ ¯GR(ω + i0)

    Start from a guess for¯Σint(ω)(if you are at the very first timestep, t = 0, take for example the equilib- rium ¯Σint, otherwise start from ¯Σint(ω) calculated at the previous timestep) and solve the steady-state equation for ¯GR(ω), ¯GR(ω) = [ω + i0+ − Hloc(t) − ¯∆R(ω) − ¯ΣR int(ω)]−1. (21) in order to determine ¯A(ω) = − 1 π ℑ ¯GR(ω + i0). We recall tha...

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    Determine the lesser Green’s function from the given distribution function, using the steady-state variant of the fluctuation-dissipation theorem: ¯G<(ω) = 2πi ¯F (ω) ¯A(ω) (22) In NESS, ¯F (ω) does not need to be a Fermi-Dirac distribution and, indeed, in general it is not

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    Use the self-consistency Eq. (9) to fix the hybridiza- tion function of the effective steady state impurity model, ¯∆R,<(ω) = t2 h ¯GR,<(ω) + Γ(ω) (23) where Γ(ω) is the additional contribution to the hybridization function that implement to simulate photoexcitation, see Appendix E. 5 0 20 40 60 80 100 t −0.4 −0.3 −0.2 −0.1 0.0 Ekin (a) 0 20 40 60 80 100 ...

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    Solve the impurity model. With IPT as impurity solver, we first determine¯G(ω) from ¯∆(ω), ¯GR(ω) = [ω + i0+ − Hloc(t) − ¯∆R(ω)]−1 , ¯G<(ω) = ¯GR(ω) ¯∆<(ω) ¯GA(ω) , (24) then Fourier transform to relative time, evaluate the steady-state version of Eq. (14), and transform back to frequency space to obtain¯ΣR,< U (ω)

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    (15), becomes ¯ΣR,< γ (ω) = γ(t) 1 2π Z dω ¯GR,<(ω) (25)

    In the time-translational invariant case (NESS loop), the purely dissipative part of the self-energy, Eq. (15), becomes ¯ΣR,< γ (ω) = γ(t) 1 2π Z dω ¯GR,<(ω) (25)

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    Set ¯Σint(ω) = ¯ΣU (ω) + ¯Σγ(ω), and iterate steps1) to 5) until convergence. The DMFT self-consistency serves as a way to eval- uate ΣNESS[FG(·, t)] (as well as ANESS[FG(·, t)] and ∆NESS[FG(·, t)]). The differential equation (19) is then solved using a Runge-Kutta algorithm i...

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    Perturbative expansion in terms of γ At first order in the dissipation strengthγ, , the cor- rection to the Green’s function can be decomposed into two distinct contributions, G(1)αβ σ (t, t′) = G(1)αβ σ,jump(t, t′) + G(1)αβ σ,NH (t, t′) (B5) where G(1)αβ σ,jump arises from th...

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