{"id":"3ab6c979-57de-4e4e-bfeb-9b5265a5b7fa","arxiv_id":"1908.01213","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The dissipative neutral edge mode is predicted to carry a heat current of (σxy/2πσxx) times the flux quantum, with the same fraction at filling factors 1 and 2.","lead":"This paper calculates heat flow along a quantum Hall edge when the edge contains a dissipative compressible strip. It predicts the lowest neutral edge mode carries a fraction of the standard heat quantum, which could explain why a 2010 heat transport experiment saw about 13% less heat than expected.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The non-quantized heat current is controlled by the UV cutoff region, and the ν=2 result in Eq. (27) is asserted rather than derived from the Appendix response functions; both need explicit verification.","rationale":"The paper is a good-faith low-energy hydrodynamic model with a clear FDT-based calculation at ν=1 and an explicit, if incomplete, generalization to ν=2. The model is internally consistent and the authors transparently state the main limitations: the σxx≫σxy assumption, the necessity of the 1/ξ cutoff, and the lack of a microscopic dissipation model. The reader's conditional verdict is therefore appropriate. The most load-bearing concern is that the non-quantized heat current is not a robust low-energy consequence: it arises from integrating over the full range up to the UV cutoff, and the authors themselves note that removing the cutoff restores quantization. This makes the claimed universality of σxy/(2πσxx) dependent on an unverified cancellation and on the ν=2 calculation, which is sketched rather than carried out. The proposed concrete test directly checks both the cancellation and the ν=2 result, so it would settle whether the central claim holds. I do not see a reason to change the reader's conditional verdict; the concern strengthens the need for verification but does not, by itself, demonstrate an error.","tokens_in":11112,"tokens_out":21414,"duration_ms":220471,"concrete_test":"Perform a symbolic or numerical evaluation of the heat current J_E in Eq. (A1) using the response functions (A7)-(A13) and the determinant (A14)-(A15), expanding to first order in σxy/σxx under T≪σxxε0/σxy. Verify that the result is exactly [2 + σxy/(2πσxx)] Jq and is independent of the velocities v1...v4 and of the cutoff ξ. As a cross-check, repeat the ν=1 calculation from Eq. (18) with the k-integration cutoff sent to infinity: confirm that quantization is restored and identify which terms vanish or change; if either calculation leaves a dependence on ξ or vσ, the claimed universality of Eqs. (19) and (27) fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the dissipative AG mode carries a universal fraction σxy/(2πσxx) of the heat flux quantum rests on the treatment of the high-energy cutoff. In Sec. IV, Eq. (18) integrates k only over |k|≤1/ξ, and the authors state that extending the integral to infinity restores full quantization. Thus the non-quantized correction is not a protected low-energy property; it is dominated by the boundary of the hydrodynamic regime, and any physics above 1/ξ could change the coefficient. The claimed cancellation of velocities and cutoff in Eq. (19) is not shown step-by-step, and an independent evaluation of Eq. (18) is needed to confirm that the leading-order result really is independent of vσ and ξ. At ν=2, the situation is less supported: Appendix A writes down the response functions and determinant, but the actual integration yielding Eq. (27) is described only as 'following this strategy one can discover the correction'. Since the experimental comparison and the headline universality rely on this unshown algebra, the central result is not yet fully verified even within the model's assumptions. The σxx≫σxy expansion is also uncontrolled from a microscopic standpoint, but the cutoff sensitivity and the missing ν=2 derivation are the more direct obstacles to accepting Eqs. (19) and (27).","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a low-energy effective model of a dissipative compressible strip at the edge of an integer quantum Hall system. Dissipation is modeled through a finite diagonal conductivity sigma_xx in the strip, and the lowest hydrodynamic (Aleiner-Glazman) neutral mode acquires an overdamped spectrum. The authors compute the heat current carried by this mode using response functions and the fluctuation-dissipation theorem. At nu=1 they claim the dissipative mode carries J_sigma = (sigma_xy/(2 pi sigma_xx)) J_q, and at nu=2 they claim the total heat current is J_E = [2 + sigma_xy/(2 pi sigma_xx)] J_q. The paper suggests these dissipative modes explain the missing heat current observed by le Sueur et al. (PRL 105, 056803 (2010)).","tokens_in":11362,"tokens_out":7302,"duration_ms":76853,"significance":"If the central claim is correct, the paper provides a concrete mechanism for the observed breakdown of heat-current quantization in integer quantum Hall edges and offers a potential explanation for the elusiveness of hydrodynamic neutral modes. The model is explicit, the FDT-based response-function formalism is appropriate, and the authors honestly flag the need for a microscopic model of dissipation. However, the significance is conditional: the claimed correction is dominated by the high-energy cutoff region rather than being a protected low-energy property, and the paper's own discussion concedes that the exact numerical prefactor depends on interaction details. The experimental consistency check is also not a parameter-free test, since the ratio sigma_xy/sigma_xx is an input parameter. These issues must be resolved before the universality claim can be accepted.","major_comments":[{"comment":"The evaluation leading to Eq. (19) is not shown in sufficient detail, and the claim that all auxiliary parameters cancel is not demonstrated. A straightforward evaluation under the stated wide-Lorentzian approximation and a sharp cutoff at |k|=1/xi gives a prefactor of order 3/(2 pi^2), not exactly 1/(2 pi), so the exact coefficient depends on how the cutoff and the Lorentzian tails are treated. This is not a purely cosmetic issue, because the discussion section states that \"the exact numerical prefactor depends on the interaction details,\" which appears to contradict the universality claimed in Eq. (19). The authors should provide the full step-by-step evaluation of the integral and clarify the range of validity of the stated cancellation.","section":"Eq. (18)-(19), Sec. IV"},{"comment":"The nu=2 heat current result is asserted rather than derived. After writing the response functions and the determinant, the appendix ends with \"Following this strategy one can discover the correction sigma_xy/(2 pi sigma_xx) J_q.\" This is the key result used for the experimental comparison, and the relevant algebra is not shown. The authors should either display the full computation, including how the cross-correlators combine to produce exactly the same correction as at nu=1, or provide a reproducible symbolic calculation.","section":"Appendix A, Eq. (27)"},{"comment":"The claimed consistency with the 13% heat deficit in Ref. [13] appears numerically inconsistent with the central expansion assumption. If the deficit is interpreted as sigma_xy/(2 pi sigma_xx) = 0.13, then sigma_xy/sigma_xx is about 0.8, which violates the assumption sigma_xx >> sigma_xy used throughout to expand in sigma_xy/sigma_xx and to treat the neutral mode as overdamped. The authors should state explicitly how the measured 13% is normalized and clarify whether the inferred ratio lies within the regime where their leading-order result is controlled; otherwise the comparison to experiment is not a meaningful consistency check.","section":"Introduction and Sec. VI"},{"comment":"The paper correctly notes that extending the k integral in Eq. (18) to infinity restores full quantization, which means the non-quantized correction is dominated by the boundary of the hydrodynamic regime. Since the coefficient is set by physics at k ~ 1/xi, the prediction is not protected from microscopic details above the cutoff. This limitation is acknowledged in the discussion, but it directly affects the headline claim of universality; the paper should quantify the sensitivity of Eq. (19) to the cutoff profile and state explicitly that the result is not a universal low-energy prediction in the usual sense.","section":"Sec. IV, renormalization of quantization"}],"minor_comments":[{"comment":"There are several typos, e.g., \"seams reasonable\" near Eqs. (3)-(7) should read \"seems reasonable.\"","section":"General"},{"comment":"The parameter delta is introduced as the effective width of the charge density in the edge channels, but its precise definition and relation to the strip width xi are not clear; a short clarifying sentence would help.","section":"Sec. II, Fig. 2"},{"comment":"The upper limit of the frequency integral is written as T, but the integrand does not show the Bose factor or the vacuum subtraction that appears in Eq. (17); the authors should align the notation with the FDT formula in Eq. (15).","section":"Eq. (18)"},{"comment":"The phrase \"the exact numerical prefactor depends on the interaction details\" should be reconciled with Eq. (19) and with the abstract's claim that the carried portion is the same at nu=1 and nu=2; as written, the two statements require qualification.","section":"Sec. VI"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is honest about its limitations, but the central claim rests on an unshown integral evaluation at nu=1, an unshown derivation at nu=2, and an experimental comparison that appears to require sigma_xy/sigma_xx of order one, in tension with the sigma_xx >> sigma_xy expansion. These are fixable in a revision if the authors can supply the missing algebra and a clear statement of the parameter regime. If the numerical prefactor turns out to depend on cutoff details, the title-level claim of universality will need to be substantially softened."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Plainly: this paper identifies a plausible culprit for the missing heat in the ν=2 experiment and predicts the same fractional deficit at ν=1. But the central result is not actually derived in front of the reader, and it lives on the UV cutoff. I'd send it to referees, but I'd want the algebra shown before believing Eq. (19) and (27).\n\nThe genuinely new thing is the heat current of the overdamped Aleiner-Glazman mode. Earlier work looked at spectra and charge transport; this is the first calculation of the energy carried by that mode, including the ν=2 generalization and the claim that the fraction is the same at both fillings. That is a solid increment over their own hydrodynamic model (Ref 39), and the paper is honest that a microscopic model of dissipation is still missing.\n\nThe soft spots are real and in proportion. First, the step from Eq. (18) to (19) is skipped. The integral over k is dominated by the cutoff region; the authors assert that velocities and cutoff cancel, but the reader cannot check that from the text. Second, the ν=2 result, Eq. (27), is asserted. Appendix A sets up response functions and the determinant, but the actual integration that yields the correction is described as 'following this strategy one can discover' – that is not a derivation, it's a promissory note. Third, the ratio σxy/σxx is an input, not computed or measured, so matching the 13% deficit is a consistency check, not a parameter-free prediction. Fourth, the cutoff sensitivity is acknowledged: extending the k integral to infinity restores full quantization. That means the non-quantized piece is not a protected low-energy property; the answer depends on physics above 1/ξ. None of these are fatal, but together they mean the paper's central quantitative claims are not yet verified within the model's own assumptions.\n\nWho is this for? People working on quantum Hall edge heat transport, and especially anyone trying to explain the le Sueur result. It deserves a serious referee, not a desk reject. The right referee ask is: show the integration for (18) and for (27), and discuss how robust the fraction is to the shape of the cutoff. If the algebra holds, this is a useful paper.","headline":"Plausible but unverified: the dissipative AG mode's heat fraction is a real idea, but both key equations are asserted and cutoff-sensitive.","tokens_in":11933,"tokens_out":2131,"would_cite":true,"duration_ms":21875,"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":"Dissipative neutral modes carry a fixed fraction of the quantum Hall heat flux quantum.","keywords":["quantum Hall edge","heat current","heat flux quantum","dissipative compressible strip","hydrodynamic neutral modes","fluctuation-dissipation theorem","integer quantum Hall effect"],"falsifier":"Measure the total heat current of a clean integer quantum Hall edge at $\\nu=1$ or $\\nu=2$ while tuning the compressible strip, for example by gate voltage or magnetic field to move the local $\\sigma_{xx}$ peak. If the heat current remains exactly $J_q$ (at $\\nu=1$) or $2J_q$ (at $\\nu=2$) even when a dissipative strip is present, or if the deficit does not scale with $\\sigma_{xy}/\\sigma_{xx}$ as predicted, the dissipative-neutral-mode explanation is ruled out. A $\\nu=1$ measurement is the cleanest test, since the model predicts only a single fractional correction $(\\sigma_{xy}/2\\pi\\sigma_{xx})J_q$ on top of the quantized charged mode.","tokens_in":10867,"feed_emoji":"🔥","tokens_out":10032,"duration_ms":81449,"temperature":0.7,"pith_summary":"At integer quantum Hall fillings, a clean edge transports heat in exact quanta even when additional neutral modes are present. This paper argues that if the edge hosts a compressible strip—a dissipative region with a finite diagonal conductivity $\\sigma_{xx}$—the lowest hydrodynamic neutral mode becomes overdamped and carries only the fraction $\\sigma_{xy}/(2\\pi\\sigma_{xx})$ of one heat flux quantum $J_q=\\pi T^2/12$. Because the lowest mode carries the same fraction at both $\\nu=1$ and $\\nu=2$, the total heat current becomes $(1+\\sigma_{xy}/2\\pi\\sigma_{xx})J_q$ at $\\nu=1$ and $(2+\\sigma_{xy}/2\\pi\\sigma_{xx})J_q$ at $\\nu=2$. This offers a concrete explanation for the missing heat flux seen in the $\\nu=2$ heat transport experiment reported in Ref. [13], and it makes heat transport a probe of the dissipative properties of the edge. The authors stress that a microscopic model of dissipation, beyond their low-energy effective theory, is still needed to confirm the prediction.","feed_headline":"Heat transport at quantum Hall edges loses exact quantization","feed_subtitle":"A dissipative edge strip makes neutral modes carry the same fraction of the heat flux quantum at both filling factors.","key_machinery":"The load-bearing object is a simplified electrostatic model of the dissipative compressible strip: the Hall-conductivity profile $\\sigma_{xy}(y)$ has a half-jump of width $\\xi$, and the strip carries a constant diagonal conductivity $\\sigma_{xx}$. Charged and neutral charge amplitudes live on the two boundaries of the strip; the neutral mode acquires a dominant dissipative part $-2i(\\sigma_{xx}/\\sigma_{xy})\\varepsilon_0$ with $\\varepsilon_0=2v_\\sigma/\\xi$ acting as the high-energy cutoff. The heat current is computed as an integral of density-density correlation functions obtained from the equations of motion through the fluctuation-dissipation theorem; the same machinery is repeated for the three amplitudes at $\\nu=2$, where the overdamped mode mixes with the two underdamped ones and contributes the same fractional heat current.","core_discovery":"The paper's central claim is that dissipation inside the compressible edge strip removes the exact quantization of heat current at integer quantum Hall fillings. Modeling the strip as a symmetric jump in the Hall-conductivity profile with a large diagonal conductivity $\\sigma_{xx}$, the authors find two modes: a charged edge mode that is insensitive to dissipation and carries exactly one heat flux quantum, and a hydrodynamic neutral mode with spectrum $\\omega_\\sigma = k v_\\sigma - 2i(\\sigma_{xx}/\\sigma_{xy})\\varepsilon_0$, i.e. an overdamped mode. Its contribution to the heat current, calculated from fluctuation-dissipation correlations, equals $(\\sigma_{xy}/2\\pi\\sigma_{xx})J_q$ at $\\nu=1$; repeating the calculation for $\\nu=2$, where the overdamped mode couples to the two underdamped modes, gives the same fractional contribution on top of the two quanta carried by those modes. All auxiliary parameters—velocities, interaction details, and the cutoff—drop out of the leading-order answer, leaving only the conductivity ratio $\\sigma_{xy}/\\sigma_{xx}$.","pith_inferences":["If a microscopic derivation supplied $\\sigma_{xx}/\\sigma_{xy}$ as a function of gate voltage and magnetic field, the heat-deficit measurement would become a quantitative estimator of that ratio; the model itself does not predict the ratio.","The same dissipative-strip mechanism could in principle affect heat transport at other integer fillings where a compressible strip forms, with the fractional correction set by the local conductivity ratio; the paper only works out $\\nu=1$ and $\\nu=2$.","Because the correction comes from wavevectors all the way up to the cutoff, a fully microscopic treatment that changes the high-energy behaviour could alter the numerical prefactor; the paper explicitly leaves this open.","A clean $\\nu=1$ heat-current measurement would give the sharpest test: there the prediction is a single fractional contribution on top of the quantized charged mode, with no other modes to disentangle."],"forward_implications":["At $\\nu=1$ the total heat current is predicted to be $(1+\\sigma_{xy}/2\\pi\\sigma_{xx})J_q$ rather than exactly $J_q$.","At $\\nu=2$ the total becomes $(2+\\sigma_{xy}/2\\pi\\sigma_{xx})J_q$, reproducing the qualitative 13% deficit seen in the experiment reported in Ref. [13].","The fractional correction is universal in the model: velocities, interaction details, and the cutoff scale $1/\\xi$ all cancel, so the same ratio $\\sigma_{xy}/(2\\pi\\sigma_{xx})$ controls both fillings.","The overdamped neutral mode is invisible to charge transport but contributes to heat transport, so heat measurements become a direct probe of the strip's diagonal conductivity.","For large $\\sigma_{xx}/\\sigma_{xy}$ the correction is small and quantization is approximately restored; the exact value of the measured deficit sets the conductivity ratio."],"supporting_citations":[{"why":"The $\\nu=2$ heat transport experiment whose observed deficit from the quantized value motivates and anchors the model.","marker":"[13]"},{"why":"Introduced the hydrodynamic neutral modes in a compressible strip that the present model extends by adding dissipation.","marker":"[34]"},{"why":"Reported a dissipative correction in the neutral-mode spectrum at $\\nu=2$, used to support the overdamped-mode spectrum of the model.","marker":"[38]"},{"why":"Experimental measurements of the $\\sigma_{xx}$ peak location used to justify modeling the strip as a symmetric half-jump in $\\sigma_{xy}$.","marker":"[41]"}],"fun_headline_variants":["Dissipative edge ruins heat quantization in quantum Hall","Heat current loses exact quantization at dissipative Hall edge","Quantum Hall heat flow breaks quantization via dissipation","Dissipative modes yield same heat quantum fraction at nu=1,2"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central result collapses if the compressible strip does not satisfy $\\sigma_{xx}\\gg\\sigma_{xy}$, and the non-quantized value also requires the finite high-energy cutoff $1/\\xi$; if the wave-vector integral is extended to infinity, quantization is restored.","fun_headline_variants_meta":{"raw":{"variants":["Dissipative edge ruins heat quantization in quantum Hall","Heat current loses exact quantization at dissipative Hall edge","Quantum Hall heat flow breaks quantization via dissipation","Dissipative modes yield same heat quantum fraction at nu=1,2"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000506,"raw_usage":{"total_tokens":2482,"prompt_tokens":975,"completion_tokens":1507,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":591,"completion_tokens_details":{"reasoning_tokens":1441}},"tokens_in":591,"tokens_out":1507,"duration_ms":11673,"temperature":1.0,"reasoning_tokens":1441,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T15:19:52.856117+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the total heat current of a clean integer quantum Hall edge at $\\nu=1$ or $\\nu=2$ while tuning the compressible strip, for example by gate voltage or magnetic field to move the local $\\sigma_{xx}$ peak. If the heat current remains exactly $J_q$ (at $\\nu=1$) or $2J_q$ (at $\\nu=2$) even when a dissipative strip is present, or if the deficit does not scale with $\\sigma_{xy}/\\sigma_{xx}$ as predicted, the dissipative-neutral-mode explanation is ruled out. A $\\nu=1$ measurement is the cleanest test, since the model predicts only a single fractional correction $(\\sigma_{xy}/2\\pi\\sigma_{xx})J_q$ on top of the quantized charged mode.","supporting_citations":[{"cited_title":"le Sueur , author C","cited_arxiv_id":null,"evidence_quote":"The $\\nu=2$ heat transport experiment whose observed deficit from the quantized value motivates and anchors the model."}],"review_version":1}