{"id":"be66171e-8652-4b80-9f3f-44864379c245","arxiv_id":"2501.05346","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A real-frequency TPSC+DMFT calculation on the square-lattice Hubbard model qualitatively reproduces pseudogap, Mott insulating, and Fermi-arc physics.","lead":"This paper tests a hybrid calculation method, TPSC+DMFT, on the two-dimensional Hubbard model, a standard model for high-temperature superconductors. The method combines local and nonlocal electron correlations, and the authors show it can reproduce pseudogaps and Fermi arcs seen in cuprate materials.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The method's central claim rests on the NCA double occupation used to fix Usp/Uch; since NCA is acknowledged to underestimate double occupation, the pseudogap and Fermi arcs may be solver artifacts until benchmarked with an accurate impurity solver.","rationale":"I agree with the reader that the NCA double occupation is the weakest assumption, and therefore set agreement_with_reader to 'agree'. The concern is load-bearing because the entire nonlocal correction in TPSC+DMFT is controlled by Usp and Uch, which are determined by that single local quantity. The authors explicitly flag the NCA limitation and point to future higher-order solvers, which confirms that this is not a settled point. My proposed test is a direct quantitative benchmark that would settle whether the headline pseudogap and Fermi-arc results survive with an accurate double occupation. Since the reader's verdict is already CONDITIONAL and this concern does not, by itself, invalidate the qualitative demonstration, the appropriate verdict remains CONDITIONAL. I therefore recommend UNCHANGED.","tokens_in":19734,"tokens_out":7298,"duration_ms":75993,"concrete_test":"Recompute the DMFT step for U=8, t'=-0.3t, 10% hole doping, T=0.05 using a quantitatively reliable impurity solver (for example CT-HYB on the Matsubara axis with analytic continuation, or a higher-order steady-state solver such as the one in Ref. 40), extract the double occupation, and feed it through the identical one-shot TPSC+DMFT procedure to obtain Usp, Uch and the Fermi-surface spectral function. If the double occupation changes by more than a few percent and the antinodal pseudogap or the Fermi arc is no longer present or moves substantially, the central claim is solver-dependent. If the features persist with similar vertices, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that one-shot TPSC+DMFT gives a meaningful description of the moderately correlated half-filled system and the doped Mott insulator, with pseudogap, Mott gap, and Fermi-pocket-to-arc evolution. The chain of reasoning has a single most fragile link: the TPSC vertices Usp and Uch are fixed by substituting the DMFT double occupation into the sum rules in Eq. (12), and these vertices enter directly into the nonlocal self-energy in Eq. (17) that produces the pseudogap and momentum-dependent Fermi surface. The DMFT double occupation is computed with the NCA impurity solver, which the authors themselves state 'tends to underestimate the double occupation' and overestimates correlation strength (Sec. III A). The authors deliberately do not compensate by reducing U, to avoid adjustable parameters. Because Uch is already very large (269.89 at U=8 half-filling and 134.88 at 5% doping), even a moderate relative error in the double occupation can substantially change the vertices and hence the nonlocal self-energy. The paper's validation is qualitative, comparing visual features with cluster DMFT and ARPES rather than performing a same-parameter quantitative benchmark. Until the NCA bias is quantified, the possibility remains that the pseudogap and Fermi arcs are artifacts of an overestimated correlation strength rather than genuine nonlocal physics.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a real-frequency implementation of TPSC+DMFT for the square-lattice Hubbard model. In the proposed scheme, a DMFT calculation with an NCA impurity solver provides the local self-energy and the double occupation; the double occupation fixes the TPSC spin and charge vertices through the sum rules, and the TPSC nonlocal self-energy is added one-shot to the DMFT Green's function. Results are reported for half-filling at U=4, 6, 8 and for hole doping from 5% to 20% with t'=-0.3t and U=8. The authors observe pseudogap features at moderate coupling, a Mott gap at strong coupling, and a Fermi-pocket-to-arc evolution upon doping, and they conclude that one-shot TPSC+DMFT is a versatile and efficient bridge between weak- and strong-coupling descriptions of the Hubbard model.","tokens_in":20010,"tokens_out":6056,"duration_ms":55707,"significance":"If the claims are correct, the paper provides a computationally efficient real-frequency hybrid that avoids analytic continuation and offers direct access to spectral functions and Fermi surfaces. The strengths are the real-frequency implementation, the use of sum rules rather than fitted parameters, and the systematic comparison of TPSC, DMFT, FLEX, and TPSC+DMFT within a common setup. However, the central claim rests on the accuracy of the NCA double occupation and on qualitative comparisons with cluster DMFT and ARPES. No same-parameter quantitative benchmark is provided, and the acknowledged NCA bias could change the vertices and the nonlocal self-energy enough to alter the pseudogap and Fermi-arc features. The paper is therefore a useful methodological contribution whose main physical conclusions are not yet fully established.","major_comments":[{"comment":"The sum rules in Eq. (12) are closed with the DMFT double occupation, and the resulting vertices Usp and Uch enter directly into the nonlocal self-energy in Eq. (17). In Section III A the authors state that the NCA solver 'tends to underestimate the double occupation' and overestimates correlation strength, yet they deliberately do not compensate by reducing U. For half-filling at U=8 the charge vertex is Uch=269.89 (Table I), and for 5% hole doping it is 134.88 (Table II). Because the charge vertex is so large, a moderate error in the double occupation can change the susceptibilities and the nonlocal self-energy substantially. The authors should quantify this sensitivity, for example by benchmarking the NCA double occupation against a higher-order steady-state impurity solver (refs. 40,41) or by repeating the TPSC+DMFT calculation with a DMFT U reduced within the stated NCA bias and showing that the pseudogap and Fermi-arc features are stable.","section":"§III A, Table I, Eq. (12)"},{"comment":"The paper's central claim that one-shot TPSC+DMFT gives a meaningful description is supported only by visual comparison with cluster DMFT and ARPES, not by a quantitative same-parameter benchmark. For example, the Fermi surface of the 5% doped system in Fig. 10(c) shows discontinuities, and the text acknowledges that TPSC+DMFT 'struggles in the underdoped regime'; the comparison with cluster DMFT results (Refs. 46,53) is qualitative. A direct benchmark at the same U, T, t', and doping—e.g., the antinodal spectral weight as a function of doping or the momentum dependence of the self-energy along the Fermi surface—would establish whether the pseudogap and Fermi-arc evolution are quantitatively reliable or mainly artifacts of the approach. Without such a benchmark, the main physical conclusions remain suggestive.","section":"§III A–C, Figs. 3, 6, 9, 10"},{"comment":"For U=6 and U=8, the authors note that there may be two pairs of solutions for Usp and Uch and select the solution satisfying Usp<U and continuously connected to U=4. Since the selected vertices determine the nonlocal self-energy through Eq. (17), the results in Fig. 7 depend on this branch choice. The authors should justify why the discarded branch is unphysical and show that the main features (Mott gap, pseudogap, satellite structures) are robust with respect to the branch selection.","section":"§III B, text before Fig. 7"},{"comment":"The one-shot character is a central methodological assumption: iterating the loop with NCA fails to converge, and the self-consistent variants in Appendix A lose the pseudogap and almost coincide with DMFT. This leaves open whether the pseudogap is a robust feature of the combined scheme or an artifact of stopping before feedback. A useful test would be to replace G(1) in Eq. (17) with the DMFT Green's function in the TPSC self-energy and check whether the qualitative conclusions survive; alternatively, the authors could provide a convergence diagnostic or a physical argument for why the one-shot stopping point is preferred.","section":"§II D, Appendix A"}],"minor_comments":[{"comment":"The text says 'TPSC+DMFT spectra, shown in Figs. 7(d), 7(f), and 7(i)', but the TPSC+DMFT panels in Fig. 7 are (c), (f), and (i), not (d), (f), and (i). Please correct the cross-reference.","section":"§III B, text after Fig. 7"},{"comment":"The bath parameters Γ=0.05 and D=32 are introduced to stabilize the chemical potential, but their effect on the presented spectra is not discussed. A brief statement that the results are insensitive to these parameters, or a plot for a different Γ value, would clarify that the bath does not alter the physics.","section":"§II F"},{"comment":"The caption says TPSC+DMFT '(same as TPSC)', which is correct because the nonlocal self-energy is identical, but readers may be confused about whether the local self-energy is included. Please state explicitly in the text that Fig. 4 shows only the nonlocal part, with the local part subtracted.","section":"Fig. 4 caption"},{"comment":"Several equations contain apparent rendering artifacts in the arXiv text (e.g., Eq. (1) and Eq. (9)); please ensure the published version uses clean typeset notation.","section":"General"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a useful method paper. The real contribution is a real-frequency implementation of TPSC+DMFT that pushes the combination into moderate-to-strong coupling and doped Mott territory, and it produces the expected qualitative physics: pseudogap at half-filling, Mott gap at large U, Fermi pockets evolving into arcs with hole doping. That is genuinely useful for people working on Hubbard model methods, especially because the spectra are computed directly on the real axis with no analytic continuation. The authors also do a service by showing that self-consistent TPSC+GG and TPSC+GG+DMFT variants lose the pseudogap, a nontrivial negative result that clarifies why the one-shot scheme is the sensible choice.\n\nThe method itself is not new, and the authors say so; this is an extension of Refs 22-24. What is new is the real-frequency implementation and the systematic study of strong coupling and doping. The physics is consistent with cluster DMFT and ARPES at a qualitative level, and the discussion of which spectral features come from spin versus charge fluctuations is clear and well documented. The cost is low and the momentum resolution is high.\n\nThe soft spot is the NCA impurity solver. The authors acknowledge NCA underestimates the double occupation and overestimates correlation strength, and because the TPSC vertices Usp and Uch are fixed by that double occupation, the nonlocal self-energy that generates the pseudogap and Fermi arcs inherits the solver bias. Uch is huge (269 at U=8, half-filling), so the sensitivity is real. Choosing not to compensate to avoid adjustable parameters is defensible, but it leaves the central claim conditional. Until the same calculation is benchmarked against a more accurate impurity solver or a quantitatively comparable cluster method for identical parameters, the pseudogap and arcs could be partly solver artifacts. This is a genuine concern, not a manufactured one, and it is the main reason the paper is a conditional rather than a clean accept.\n\nThe paper is honest, the method is cheap, and the real-frequency implementation is valuable on its own. It deserves a serious referee; the natural request would be a quantitative benchmark for at least a few parameter points. I would take it to reading group and would cite it if I worked on TPSC-style methods.","headline":"A useful real-frequency TPSC+DMFT implementation with clear qualitative physics, but the acknowledged NCA solver bias and missing quantitative benchmark keep the central claim conditional.","tokens_in":20520,"tokens_out":2727,"would_cite":true,"duration_ms":24737,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["71.10.Fd","71.27.+a","71.30.+h"],"model":"deepseek-v4-flash","headline":"TPSC+DMFT at the one-shot level reproduces the pseudogap, the Mott insulator, and the doping-driven Fermi-pockets-to-arcs crossover in the square-lattice Hubbard model.","keywords":["Hubbard model","TPSC+DMFT","pseudogap","Fermi arcs","Mott insulator","spin fluctuations","real-frequency methods","square lattice"],"falsifier":"Take the half-filled $U=4$, $t'=0$, $T=0.25$ case and replace the NCA double occupation in the TPSC sum rules with a value from a high-precision local or cluster solver; if $U_{\\rm sp}$ and $U_{\\rm ch}$ change appreciably and the antinodal spectral-weight suppression at $X$ disappears, the pseudogap is a solver artifact rather than nonlocal spin physics. Repeat the test at 10% doping by comparing the computed Fermi arc length with an independent cluster result.","tokens_in":19516,"feed_emoji":"⚛️","tokens_out":16295,"duration_ms":141333,"temperature":0.7,"pith_summary":"This paper sets out to show that a one-shot hybrid of Dynamical Mean-Field Theory (DMFT), which supplies local correlations, and Two-Particle Self-Consistent theory (TPSC), which supplies nonlocal spin and charge fluctuations, can describe the two-dimensional Hubbard model in and beyond the moderately correlated regime. The central claim is that using DMFT's double occupation to fix TPSC's effective vertices, then adding TPSC's momentum-dependent self-energy to DMFT's local self-energy, reproduces the pseudogap (a partial suppression of low-energy spectral weight at the antinode), the Mott insulator (an insulating state driven by electron repulsion) at large interaction strength, and the doping-driven evolution of Fermi pockets into Fermi arcs. A reader should care because the calculation runs entirely on the real-frequency axis, avoiding analytic continuation, and is far cheaper than cluster methods that have previously produced these features. If the claim holds, TPSC+DMFT is a practical bridge between weak- and strong-coupling physics of a central model of correlated electrons.","feed_headline":"Hybrid Hubbard solver captures pseudogap, Mott gap, and Fermi arcs","feed_subtitle":"A cheap one-shot mix of local and nonlocal correlations reproduces cluster and photoemission results.","key_machinery":"The load-bearing object is the TPSC nonlocal self-energy, built from renormalized spin and charge susceptibilities $\\chi_{\\rm sp}$ and $\\chi_{\\rm ch}$. TPSC replaces the bare interaction $U$ with two effective vertices $U_{\\rm sp}$ and $U_{\\rm ch}$, chosen so that the local susceptibilities satisfy the Pauli-principle sum rules; the double occupation entering those sum rules is supplied by DMFT rather than by the usual phenomenological Ansatz. The resulting self-energy averages longitudinal and transverse channels, $\\Sigma^C_{i,j}(t,t') = -\\frac{iU}{8} G^{(1)}_{i,j}(t,t')\\,[U_{\\rm ch}\\chi^{\\rm ch}_{j,i}(t',t)+3U_{\\rm sp}\\chi^{\\rm sp}_{j,i}(t',t)]$, and is added once to the DMFT local self-energy inside the Dyson equation. The spin-channel part of this nonlocal self-energy produces a mirrored band, an image of the noninteracting dispersion that suppresses the antinodal region and creates the pseudogap; the charge-channel part generates high-energy satellite structures. A real-frequency, steady-state implementation with a non-crossing approximation (NCA) impurity solver avoids analytic continuation and resolves spectra on a $64\\times64$ momentum grid.","core_discovery":"The central claim is that the one-shot TPSC+DMFT construction is already sufficient for a meaningful description of both moderately and strongly correlated regimes of the square-lattice Hubbard model. In the half-filled $U=4$ system at $T=0.25$, adding the TPSC nonlocal self-energy to the DMFT local self-energy suppresses spectral weight at the antinodal $X$ point while leaving the nodal region metallic, producing a pseudogap that plain DMFT lacks and that FLEX is too smooth to form. For $U=6$ and $U=8$ at half-filling, the same construction keeps the Mott gap essentially intact, with nonlocal corrections only redistributing spectral weight. In the doped Mott regime ($U=8$, $t'=-0.3t$, at 5%, 10%, and 20% hole doping), the method yields a Fermi pocket at low doping, a clear Fermi arc at 10%, and an almost full Fermi surface at 20%, in line with cluster methods and photoemission studies. The paper also reports that self-consistent variants (TPSC+GG and TPSC+GG+DMFT) lose the pseudogap and collapse toward the DMFT solution, so the one-shot character is not a numerical shortcut but part of the mechanism.","pith_inferences":["A testable extension of the paper's own caveat: if the NCA double occupation is corrected by a more accurate impurity solver, the same one-shot construction could be pushed to lower temperatures or stronger couplings, where the pseudogap is sharper and the Fermi arcs shorter.","The steep rise of the charge vertex $U_{\\rm ch}$ with underdoping (134.9 at 5% doping versus 32.5 at 20%) suggests that the upper-band distortions seen in the doped spectra are charge-channel artifacts; a natural test is to keep only the transverse spin channel below 10% doping and compare the resulting spectral functions.","The real-frequency Keldysh setup is ready in principle for nonequilibrium studies, and the missing ingredient the paper identifies is self-consistency; a partially self-consistent scheme that preserves the one-shot nonlocal vertex would open photo-doped Mott states to this method."],"forward_implications":["At half-filling with $U=4$, TPSC+DMFT predicts a pseudogap whose origin is nonlocal spin fluctuations at the antinode, while DMFT alone and FLEX do not produce this feature.","In the strongly correlated half-filled regime ($U=6$ and $U=8$), the nonlocal self-energy corrections do not destroy the Mott gap, indicating that the DMFT local physics dominates there.","In the doped Mott insulator, the method predicts a Fermi pocket at low doping that evolves into a Fermi arc and then a nearly full Fermi surface as doping increases, a sequence that can be compared directly with photoemission arc-length measurements.","Self-consistent feedback variants are contraindicated: iterating the interacting Green's function back into TPSC erases the nonlocal correlations and the pseudogap, leaving a solution close to plain DMFT.","The real-frequency implementation supplies momentum- and frequency-resolved spectra without analytic continuation, so the same setup can produce high-resolution benchmarks for other approaches."],"supporting_citations":[{"why":"Establishes the TPSC formalism, including renormalized spin and charge vertices and the sum rules, together with its real-frequency implementation.","marker":"19,20"},{"why":"Earlier TPSC+DMFT combinations restricted to weak-to-moderate coupling that this work extends toward the Mott and doped regimes.","marker":"22–24"},{"why":"Derives the longitudinal and transverse decomposition of the TPSC self-energy and documents the self-consistent feedback whose one-shot version is the paper's central scheme.","marker":"23"},{"why":"Documents the NCA solver's tendency to underestimate the double occupation, the input that the paper's weakest assumption depends on.","marker":"28"},{"why":"Provides an independent diagrammatic calculation showing the mirrored nonlocal self-energy that supports the pseudogap interpretation.","marker":"42"},{"why":"Supplies the cluster calculation of the doped Mott insulator whose Fermi pocket and arc features are used as the benchmark.","marker":"53"},{"why":"Supplies the cluster study of doping evolution whose Fermi surface results are compared with the TPSC+DMFT arcs.","marker":"54"},{"why":"Provides the cluster Fermi-surface results used for comparison at half-filling and in the doped regime.","marker":"46"},{"why":"Shows that TPSC can describe cuprate-like Fermi surfaces and the pseudogap, motivating the doped-model analysis.","marker":"21"}],"fun_headline_variants":["One-shot TPSC+DMFT maps Hubbard pseudogap to Mott arcs","One-and-done TPSC+DMFT maps Hubbard pockets to arcs","TPSC+DMFT one-shot shows Fermi arcs and pseudogap","Pocket-to-arc evolution via one-shot TPSC+DMFT"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The construction stands or falls on the DMFT double occupation computed with the non-crossing approximation (NCA) solver being accurate enough to fix the effective vertices $U_{\\rm sp}$ and $U_{\\rm ch}$; the authors themselves note that NCA tends to underestimate this double occupation and they deliberately avoid an adjustable compensation, so a quantitatively wrong value could turn the pseudogap and Fermi arcs into solver artifacts.","fun_headline_variants_meta":{"raw":{"variants":["One-shot TPSC+DMFT maps Hubbard pseudogap to Mott arcs","One-and-done TPSC+DMFT maps Hubbard pockets to arcs","TPSC+DMFT one-shot shows Fermi arcs and pseudogap","Pocket-to-arc evolution via one-shot TPSC+DMFT"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001366,"raw_usage":{"total_tokens":5548,"prompt_tokens":964,"completion_tokens":4584,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":580,"completion_tokens_details":{"reasoning_tokens":4504}},"tokens_in":580,"tokens_out":4584,"duration_ms":28655,"temperature":1.0,"reasoning_tokens":4504,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:12:13.076065+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the half-filled $U=4$, $t'=0$, $T=0.25$ case and replace the NCA double occupation in the TPSC sum rules with a value from a high-precision local or cluster solver; if $U_{\\rm sp}$ and $U_{\\rm ch}$ change appreciably and the antinodal spectral-weight suppression at $X$ disappears, the pseudogap is a solver artifact rather than nonlocal spin physics. Repeat the test at 10% doping by comparing the computed Fermi arc length with an independent cluster result.","supporting_citations":[{"cited_title":"The k-resolved spectral functions averaged over ω ∈ [−0.2, 0.2] are presented in Fig","cited_arxiv_id":null,"evidence_quote":"Derives the longitudinal and transverse decomposition of the TPSC self-energy and documents the self-consistent feedback whose one-shot version is the paper's central scheme."},{"cited_title":"To avoid adjustable parame- ters, we however prefer to use the same U as in TPSC, keeping in mind the bias from the NCA","cited_arxiv_id":null,"evidence_quote":"Documents the NCA solver's tendency to underestimate the double occupation, the input that the paper's weakest assumption depends on."},{"cited_title":"one- shot","cited_arxiv_id":null,"evidence_quote":"Shows that TPSC can describe cuprate-like Fermi surfaces and the pseudogap, motivating the doped-model analysis."}],"review_version":1}