{"id":"b3d5c99f-d22e-4cd6-9439-46717859da59","arxiv_id":"2511.10934","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":11,"one_line_summary":"iPEPS imaginary-time relaxation can extract the 2D TFIM critical field and the exponent -β/(νz) from the transient decay, but its extrapolated initial-slip exponent θ≈0.196 lies outside the quoted QMC error bar (0.209±0.004).","lead":"The paper uses a tensor-network method (iPEPS) to watch how a 2D quantum magnet relaxes in imaginary time near its critical point, and extracts critical exponents from the transient, non-equilibrium stage. It shows the method can locate the critical field and one exponent well, but the claimed match for a second exponent (θ) is weaker than stated.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The reported θ=0.1958 lies outside the QMC error bar (0.209±0.004); the extraction depends on hand-selected windows and an unspecified three-point 1/D extrapolation, so the claimed agreement and the method's robustness are not established.","rationale":"The reader's weakest assumption identifies the fitting procedure at h* with hand-selected windows and the subsequent exponent extraction as the main vulnerability. My analysis agrees: the θ value is the clearest quantitative failure—it lies outside the QMC error bar, yet the paper claims it 'agrees well.' The method's usefulness for -β/(νz) is reasonably supported (the three slopes are close to -0.518), but the initial-slip exponent is the more discriminating test because it involves a different scaling regime and is more sensitive to finite-entanglement shifts. The concrete test I propose is a straightforward check of whether the discrepancy persists when h is fixed to the known critical field and windows are systematically varied. This would settle whether the reported θ is an artifact of the selection procedure or a genuine limitation of iPEPS for early-time dynamics. Given the existing CONDITIONAL verdict, my concern does not change the overall recommendation; it reinforces the need for the authors to provide error bars and a justified extrapolation, or to benchmark on another independent method. I set verdict_should_be to UNCHANGED because the reader already made the appropriate conditional call.","tokens_in":9797,"tokens_out":4145,"duration_ms":41051,"concrete_test":"Recompute the slopes k* for D=3,4,5 at the fixed field h=3.044 (the known h_c) over a common τ window, e.g., 0.5<τ<0.84 (for D=3, extend the simulation to τ≥0.5; if necessary, use 0.3<τ<0.5 and check consistency). Then vary both window endpoints by ±20% to generate a spread of slopes for each D. Extrapolate the resulting slope sets to 1/D→0 using at least two forms (linear and quadratic in 1/D) and bootstrap to obtain error bars. If the extrapolated θ remains below 0.200 with uncertainty not overlapping 0.209(4), the discrepancy is systematic and the claim of agreement fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that iPEPS is a robust and scalable probe of dynamical critical phenomena rests on the quantitative accuracy of the extracted exponents. For the initial-slip exponent θ, the paper obtains k* = 0.12586 (D=3, window 0.2<τ<0.5), 0.17889 (D=4, window 0.5<τ<0.84), 0.1902 (D=5, same window), and then a power-law fit in 1/D gives θ≈0.19584 (Fig. 4). This is ~3σ below the QMC value 0.209(4) [10]. The discrepancy is not just statistical: the fitting procedure is circular. As the paper itself states (Sec. IV.A), h* is chosen as the field giving the 'best power law' in the log-log plot, and the slope is then fit at that same h*. For D=3, h*=3.064 differs from the known h_c≈3.044 by 0.02, so the fit is performed at an off-critical field. Corrections to scaling near but not at criticality will bend the curve, and the fitted slope depends on the chosen τ window. The windows are selected per D by eye and are not justified. The extrapolation in 1/D uses only three points with an unspecified functional form and no error estimate. Given that the resulting θ deviates from the QMC value, the paper's claim of 'good agreement' is not supported. If the method cannot reproduce θ within error bars, the broad conclusion that iPEPS reliably captures universal early-time dynamics is overstated. This is the load-bearing weak point: the exponent that would demonstrate the method's quantitative power is extracted in a way that admits systematic bias and does not match the reference value.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies imaginary-time relaxation critical dynamics of the two-dimensional transverse-field Ising model using infinite projected entangled pair states (iPEPS) with the full-update strategy, working directly in the thermodynamic limit. For a fully polarized initial state, the magnetization is claimed to decay as M(τ)∼τ^{-β/(νz)}, and the field h* giving the best power law is used to estimate the critical point and the exponent. For a nearly paramagnetic product state with small M0, the short-time growth M(τ)∼τ^θ is analyzed, and a 1/D extrapolation of the fitted slopes yields θ≈0.19584, which the authors state is in good agreement with the quantum Monte Carlo result θ=0.209(4). The paper concludes that iPEPS is a robust and scalable method for probing dynamical critical phenomena in two dimensions.","tokens_in":10384,"tokens_out":2416,"duration_ms":23597,"significance":"If the main claims were quantitatively established, the work would be a useful methodological contribution: it demonstrates that iPEPS imaginary-time evolution can access universal short-time dynamics in the thermodynamic limit, avoiding finite-size and sign-problem limitations. The extracted critical field h_c≈3.0445 from the fully polarized sector agrees very well with the known value, and the saturated-state slopes (−0.523 to −0.520) are close to the expected −0.518. These are genuine positive results. However, the central demonstration of the method's quantitative power is the initial-slip exponent θ, and the reported value 0.19584 lies outside the quoted QMC error bar 0.209(4). The extraction procedure has several uncontrolled elements, so the claimed agreement and the broad conclusion that iPEPS reliably captures universal early-time dynamics are not yet established.","major_comments":[{"comment":"The headline initial-slip exponent θ≈0.19584 disagrees with the cited QMC value θ=0.209(4) (Ref. [10]) by about 3.3σ (difference 0.0132, error 0.004). The text states this 'agrees well' and is 'consistent with the QMC estimation,' but a value outside the quoted error bar does not support that statement. Since the initial-slip exponent is exactly the quantity that would demonstrate the method's ability to capture universal short-time dynamics, this discrepancy is load-bearing and must be addressed quantitatively, e.g., by reporting uncertainty on the extrapolation and showing that the discrepancy is within the expected finite-entanglement error.","section":"Sec. IV.B, Fig. 4"},{"comment":"The extraction procedure is circular in a way that can bias the exponent: h* is selected as the field giving the 'best power law' in the log-log plot, and the slope is then fitted at that same h*. For D=3, h*=3.063, which is 0.019 away from the known h_c≈3.044, so the fit is performed off-critical. The fitting windows are also chosen per D by eye (0.2<τ<0.5 for D=3; 0.5<τ<0.84 for D=4 and D=5) with no stated criterion. Off-critical corrections to scaling and window choice can systematically bend the fitted slope. The authors should show robustness, for example by fitting at the fixed known h_c=3.044, by varying the fitting window, and by estimating the resulting spread in k*.","section":"Sec. IV.B and Fig. 3"},{"comment":"The 1/D extrapolation uses only three points (D=3,4,5) with a 'simple power-law fit' whose functional form is not specified, and no error bars are assigned to the slopes or to the extrapolated θ. Given that the D=3 point (0.12586) is far from the D=4/5 values (0.17889, 0.1902), the extrapolated θ depends sensitively on the assumed form. The authors should specify the fitting function, include uncertainties, and test sensitivity (e.g., linear in 1/D, quadratic, or excluding D=3). Without this, the claimed value θ=0.19584 is not a controlled estimate.","section":"Sec. IV.B, Fig. 4"}],"minor_comments":[{"comment":"Typo: 'Hamailtonian' should be 'Hamiltonian'.","section":"Sec. II"},{"comment":"Typo: 'preform' should be 'perform'.","section":"Sec. IV.B"},{"comment":"The y-axis is M(τ)/M0, whereas Eq. (4) writes M(τ)∼M0 τ^θ; the caption should state clearly that the plotted quantity is normalized by M0.","section":"Fig. 3"},{"comment":"The statement that the fitted slopes are 'remarkably consistent' would be stronger with error bars or a table reporting the fitting uncertainty for each k*; currently only the raw slopes are given.","section":"Sec. IV.A"},{"comment":"The exponential fit in M0 is described only briefly. It would be helpful to state its functional form and show the fitted curve parameters, since the M0→0 extrapolation is used to support the universal value.","section":"Sec. IV.B, Fig. 5"}],"recommendation":"major_revision","confidential_remarks":"The scaling theory (Refs. [8,9]) and the QMC benchmark (Ref. [10]) share a coauthor (S. Yin) with the present paper. This is not a correctness issue, but it makes the 'good agreement' claim less independent than it might appear. The more serious issue is that the reported θ is outside the quoted QMC error bar; the authors should treat the benchmark as a quantitative target rather than a qualitative reference. I would encourage the editor to ask for a reanalysis with error estimates and robustness checks before considering publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this paper does something useful — full-update iPEPS in the thermodynamic limit, showing universal short-time imaginary-time relaxation of the 2D TFIM. The saturated-state results are the strongest part: h* moves toward h_c with bond dimension and extrapolates to 3.0445; the fitted slopes are -0.523 to -0.520 versus -0.518. That is a real, reproducible-looking demonstration and the core of the paper.\n\nThe small-M0 section is where the claim runs ahead of the evidence. The initial-slip exponent is extracted by choosing h* as the field with the best power law at each D and then fitting the slope at that same h*. For D=3, h* is 3.064 versus h_c≈3.044; fitting at an off-critical field with a hand-selected τ window (0.2<τ<0.5 for D=3, 0.5<τ<0.84 for D=4/5) can bias the slope. The resulting k* values are 0.1259, 0.1789, 0.1902, and a three-point 1/D power-law extrapolation gives θ=0.19584. No error bars are reported on the slopes, no fitting form is specified, and the extrapolation has three points. The quoted QMC value is 0.209(4); 0.196 is roughly 3σ away. Calling that 'good agreement' is too strong.\n\nI do not think the method is wrong — β/(νz) and h_c come out well, and the trend of θ with D is plausibly toward the QMC value. But the specific claim that iPEPS can reliably capture universal early-time dynamics is supported only for the decay exponent, not for θ. The reference QMC value is from a coauthor's group; that is not a flaw in itself, but it means the benchmark is not independent.\n\nWho benefits: people using tensor networks for quantum critical dynamics and those wanting a sign-problem-free route to 2D scaling exponents. The paper deserves referee time; a serious referee should ask for error estimates, a defined extrapolation form, more bond dimensions, and a benchmark not tied to the author group. With those changes the θ claim might stand. As it is, conditional.","headline":"Useful demonstration that iPEPS can extract h_c and β/(νz) from imaginary-time relaxation; the claimed θ extraction is not backed up and the 'good agreement' with QMC is overstated.","tokens_in":10861,"tokens_out":2218,"would_cite":false,"duration_ms":21601,"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":"This paper claims that the transient, pre-ground-state stage of imaginary-time evolution in an iPEPS simulation of the 2D transverse-field Ising model already contains universal quantum critical scaling, from which both the critical point a","keywords":["imaginary-time evolution","infinite projected entangled pair states","transverse-field Ising model","critical dynamics","initial-slip exponent","dynamical critical exponents","quantum phase transition","tensor network"],"falsifier":"Run the D=5 simulation at the known critical field h_c = 3.044 rather than at h* = 3.051, with a fixed fitting window such as 0.5 < tau < 0.84, and check whether the extracted theta still falls within the quoted uncertainty or whether the log-log curve loses its linearity. Equivalently, a D=6 calculation whose extrapolated theta moves away from 0.209 would contradict the claimed convergence toward the universal value.","tokens_in":9683,"feed_emoji":"🧲","tokens_out":5692,"duration_ms":48834,"temperature":0.7,"pith_summary":"The paper tries to establish that universal quantum critical dynamics can be read off from the transient, pre-equilibrium stage of imaginary-time evolution, using a tensor network that works directly in the thermodynamic limit. Simulating the square-lattice transverse-field Ising model from two types of initial states, it finds clean power laws for the magnetization: a decay M ~ tau^(-beta/(nu z)) from a fully polarized start and a growth M ~ tau^theta from a nearly paramagnetic start. The extracted critical field and exponents agree with established values, with the initial-slip exponent theta extrapolating to 0.1958, close to the quantum Monte Carlo estimate 0.209(4). If correct, this means two-dimensional quantum criticality can be probed without ground-state convergence, free of the sign problem, and at modest computational cost, opening frustrated and fermionic models to dynamical criticality studies.","feed_headline":"Critical exponents emerge before a 2D magnet reaches its ground state","feed_subtitle":"Simulating 2D Ising dynamics in imaginary time yields h_c ≈ 3.0445 and θ ≈ 0.196.","key_machinery":"The scaling theory of imaginary-time relaxation near a quantum critical point: the order parameter obeys M(tau, g, M0) = b^(-beta/nu) M(tau b^(-z), g b^(1/nu), U(M0, b)), which at criticality reduces to a power-law decay for saturated initial states and to the initial-slip law M ~ M0 tau^theta for tiny M0, with theta = (x0 - beta/nu)/z. The numerical engine is the infinite projected entangled pair state (iPEPS), a tensor-network ansatz with a 2x2 unit cell, bond dimension D, and environment bond dimension chi, evolved by the full-update strategy with Trotter-Suzuki slicing. This machinery converts the universal scaling prediction into a concrete observable: the log-log slope of M(tau) at the","core_discovery":"Starting from a fully polarized state, the imaginary-time evolved magnetization obeys M(tau) proportional to tau^(-beta/(nu z)). For each bond dimension D, the transverse field h* that gives the straightest log-log curve is selected: h* = 3.064, 3.055, 3.051 for D = 3, 4, 5, with fitted slopes -0.52339, -0.52204, -0.51983, all close to the universal -0.518, and an extrapolated critical field h_c = 3.0445. Starting from a product state with tiny magnetization M0 = 0.005, the same protocol gives initial-slip growth M proportional to tau^theta with per-D slopes 0.12586, 0.17889, 0.1902 and a large-D extrapolated theta = 0.19584, consistent with quantum Monte Carlo theta = 0.209(4). The paper co","pith_inferences":["A direct consistency test would be to fix the field at the independently known h_c ≈ 3.044 rather than at the bond-dimension-dependent h*, and check whether M(tau) remains a clean power law; if it does, the h*-fitting procedure is not essential to the exponent extraction.","The roughly 6% offset between the extrapolated theta = 0.1958 and the quantum Monte Carlo theta = 0.209(4) may stem from per-D fitting-window choices; applying one fixed window across all bond dimensions would reveal whether the residual drift is systematic.","The same imaginary-time relaxation dynamics could be mirrored in real-time evolution or on quantum simulators, where discrete Trotter steps play the role of imaginary-time slices, offering a blueprint for extracting critical exponents from pre-thermal plateaus.","If the method transfers to models without a quantum Monte Carlo benchmark, it would provide estimates of z and beta/nu in frustrated or doped systems where entanglement growth currently limits tensor-network ground-state studies."],"forward_implications":["The critical point of the 2D transverse-field Ising model can be estimated as h_c ≈ 3.0445 by extrapolating h*(D) to infinite bond dimension, matching established high-precision values.","The decay exponent -beta/(nu z) remains stable across bond dimensions (around -0.52) and close to the universal -0.518, so the exponent can be extracted without first pinpointing the exact critical field.","The initial-slip exponent theta extrapolates to 0.1958, in line with the quantum Monte Carlo value 0.209(4), and improves systematically as the bond dimension grows.","Universal scaling appears in the short-time stage, so expensive ground-state convergence is unnecessary for extracting critical properties.","Because the method is sign-problem-free and operates in the thermodynamic limit, it can be extended to frustrated magnets and interacting fermionic systems where quantum Monte Carlo fails."],"fun_headline_variants":["2D Ising critical exponents found before ground state","Imaginary-time evolution reveals quantum criticality in 2D Ising","iPEPS simulation nails 2D Ising critical exponents","Before ground state: 2D magnet's critical exponents emerge","Quantum criticality emerges early in 2D Ising imaginary-time path"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The whole extraction rests on treating the slope of the magnetization curve at the field that happens to look most like a straight line as the true universal exponent, even though that field is not exactly the critical field and the fitting range changes with the numerical accuracy.","fun_headline_variants_meta":{"raw":{"variants":["2D Ising critical exponents found before ground state","Imaginary-time evolution reveals quantum criticality in 2D Ising","iPEPS simulation nails 2D Ising critical exponents","Before ground state: 2D magnet's critical exponents emerge","Quantum criticality emerges early in 2D Ising imaginary-time path"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000549,"raw_usage":{"total_tokens":2494,"prompt_tokens":813,"completion_tokens":1681,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":557,"completion_tokens_details":{"reasoning_tokens":1592}},"tokens_in":557,"tokens_out":1681,"duration_ms":10705,"temperature":1.0,"reasoning_tokens":1592,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T22:18:45.835549+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the D=5 simulation at the known critical field h_c = 3.044 rather than at h* = 3.051, with a fixed fitting window such as 0.5 < tau < 0.84, and check whether the extracted theta still falls within the quoted uncertainty or whether the log-log curve loses its linearity. Equivalently, a D=6 calculation whose extrapolated theta moves away from 0.209 would contradict the claimed convergence toward the universal value.","supporting_citations":[],"review_version":1}