{"id":"f818b49d-f36e-490c-b135-1176893ad404","arxiv_id":"2411.15863","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For the Rice-Mele pump, the heat transported in a symmetric adiabatic cycle is exactly zero even though the charge transported is quantized; at finite temperature both decrease and vanish at infinite temperature.","lead":"This paper derives exact formulas for charge, energy, and heat transported across a link of a driven one-dimensional Rice-Mele wire during an adiabatic cycle at any temperature. It finds that heat pumped per cycle is generically non-quantized and vanishes for the symmetric pump circuits that give quantized charge transport.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equation (5) omits the kinetic second-neighbor term of the energy current; Eq. (19) therefore replaces the band energy E_n(k,t) by the odd quantity Delta(t), making the zero-heat result for symmetric circuits an artifact of the truncated current.","rationale":"The charge-pumping part of the paper (Eqs. 13-17) is standard and appears sound. The problem is the energy/heat part. The claim J_E = -Delta J_p in Eq. (5) is not the commutator of H_m with H: for U=0, evaluating [L_{2m-1},L_{2m}] yields an additional -i v w(c^†_{2m-1} c_{2m+1} - H.c.) term. This is a genuine kinetic energy current; in the uniform limit it is the well-known second-neighbor operator with k-space value E_k ∂E_k/∂k. The reader's flagged ∂H_m/∂t term is also omitted, but for a closed cycle it integrates to zero because H_m(T)=H_m(0), so it is not the decisive issue. Once the kinetic term is restored, the transported energy is governed by E_n Omega_n rather than Delta Omega_n. The symmetry cancellation in Sec. V relies on Delta(t) being odd under t -> T-t, while the band energy E_n is even because it depends on Delta^2. Thus the zero-heat result is not protected by symmetry; it is an artifact of the truncated current. A direct numerical evaluation of the full expression would settle the question. Given that the central claim of the abstract depends on this incorrect operator identity, the paper cannot be accepted in its present form; rejection or major revision is warranted unless the authors can prove the kinetic term's cycle integral vanishes.","tokens_in":51,"tokens_out":35520,"duration_ms":458890,"concrete_test":"Numerically evaluate Delta E(T) for the v0=-1, v1=Delta1=1, Delta0=0 circuit using the full energy-current expression Delta E = -(1/2π) ∫_0^T dt ∫ dk Σ_n f_n E_n(k,t) Omega_n(k,t), with E_n from Eq. (8) and Omega_n from Eq. (12), and compare with Eq. (19). If the result is nonzero while Eq. (19) gives zero, the vanishing-heat claim is an artifact of the omitted kinetic term in Eq. (5). Also verify the operator identity by computing the commutator [L_{2m-1}, L_{2m}] explicitly for U=0.","verdict_should_be":"REJECT","load_bearing_attack":"Direct evaluation of the energy current from the left-half Hamiltonian H_m (Sec. II) gives, for U=0: dH_m/dt = -Delta(t) J_p - i v(t) w(t) (c^†_{2m-1} c_{2m+1} - H.c.) + ∂H_m/∂t. The second term, from [L_{2m-1},L_{2m}], is absent from Eq. (5). It is the kinetic energy current: for a uniform chain it reduces to i t^2 (c^†_{j+2} c_j - H.c.), whose k-space value is E_k ∂E_k/∂k. The ∂H_m/∂t term, which the reader flagged, integrates to zero over a closed cycle because H_m(T)=H_m(0), so it cannot rescue the claim. With this term restored, the adiabatic energy transport is controlled by E_n(k,t) Omega_n(k,t), not Delta(t) Omega_n(k,t). For the symmetric circuits of Sec. V (Delta_0=0), Delta(t) is odd under t -> T-t, while E_n = ±[v^2 + w^2 + Delta^2 + 2 v w cos k]^{1/2} is even; hence Delta Omega integrates to zero by symmetry, but E_n Omega does not (generically). The paper's headline result that heat vanishes for symmetric cycles is therefore an artifact of the truncated current operator in Eq. (5), not a property of the Rice-Mele model.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies adiabatic charge and heat pumping in the noninteracting Rice-Mele chain at finite temperature and arbitrary filling. The authors derive closed-form expressions for the transported charge and energy as double integrals over time and momentum of the Berry curvature weighted by Fermi functions. They find that at zero temperature and half filling the pumped charge is quantized for closed cycles, while the pumped heat is generally not quantized and depends on temperature; for symmetric elliptic circuits (Δ0=0) the heat transported per cycle vanishes identically. At infinite temperature or complete filling all pumped quantities vanish. The paper also discusses the difference between transport between unit cells and between sites within a unit cell.","tokens_in":10607,"tokens_out":46225,"duration_ms":374064,"significance":"If the central result is correct, it resolves a discrepancy with the earlier work of Hattori et al. and provides a practical criterion for when heat pumping accompanies topological charge pumping. The derivation is self-contained and uses standard adiabatic perturbation theory; the symmetry argument for the vanishing of heat for Δ0=0 is elegant and is supported by explicit circuit calculations. No free parameters are fitted, and the finite-temperature reduction of transport is explicitly demonstrated. The main weaknesses are technical gaps in the derivation of the heat current and in the handling of the chemical potential for arbitrary filling.","major_comments":[{"comment":"The operator identity J_Eσ = [U n_{2m,barσ} − Δ] J_pσ is not the full energy current. A direct evaluation of dH_m/dt from the continuity equation also yields a kinetic (second-neighbor) term, e.g. i v w (c^†_{2m+2} c_{2m} − h.c.) for the link between cells m and m+1. In k-space this term is proportional to sin(k) times the identity in the two-band basis, so its expectation value integrates to zero over the Brillouin zone for the thermal distributions used (which are even in k). The paper does not state this, and as written Eq. (19) follows from an operator that is only the potential part of the energy current. The authors should either derive the full energy current and show that the kinetic contribution vanishes, or explicitly restrict their claim to the potential contribution. This is load-bearing because the vanishing-heat result for symmetric cycles is obtained from Eq. (19).","section":"Section II, Eq. (5); Section III, Eq. (19)"},{"comment":"The Fermi-Dirac distribution is written as f_n(k,t) = [exp(E_n(k,t)/k_B τ) + 1]^{-1}, which sets the chemical potential to zero. The paper claims to treat arbitrary filling, but for a general chemical potential the distribution must be [exp((E_n(k,t) − μ)/k_B τ) + 1]^{-1}. As printed, Eqs. (17) and (19) are valid only at half filling (μ = 0). This gap affects the claims in the abstract and in Section III about arbitrary filling and temperature; the authors should introduce μ explicitly and state which results are restricted to half filling.","section":"Section III, Eq. (16)"},{"comment":"The expression for the Berry curvature is stated without derivation. Using the convention d = (v + w cos k, w sin k, Δ), the printed formula is consistent with the general two-band formula, and no sin(k) term is missing; the sin^2(k) contributions cancel after the dot product with d. The authors should include a brief derivation or at least state the convention for d_y, so that readers can verify the expression and the subsequent even/odd symmetry arguments.","section":"Section III, Eq. (12)"}],"minor_comments":[{"comment":"The sentence 'We find that quantized transport is lost except in trivial cases' is misleading, because the paper shows that charge transport remains quantized at zero temperature and half filling for the usual circuits; the loss of quantization applies mainly to heat transport and to charge transport at finite temperature. Please rephrase to avoid confusion.","section":"Abstract"},{"comment":"The statement that the results are only weakly dependent on the thermalization assumption is supported only for the energy transport in one circuit. A corresponding comparison for the finite-temperature charge transport would strengthen this claim, or the authors should state the range of parameters for which the insensitivity was checked.","section":"Section V, Figs. 6 and 7"},{"comment":"In the discussion of energy conservation, the text notes that the changes in energy on the two sides of the link are identical for U = 0; this point is correct but would benefit from a more explicit statement of the sign convention used for the currents, since J_p is defined as the rate of change of the left-region particle number.","section":"Section II"},{"comment":"The phrase 'provide and expression' contains a typo; it should read 'provide an expression'.","section":"Section III, after Eq. (18)"}],"recommendation":"major_revision","confidential_remarks":"This manuscript revisits a recent PRB paper by Hattori et al. and reaches a different conclusion about heat pumping, so the fit with the journal is appropriate if the technical gaps are fixed. The two major comments are both fixable within the manuscript's scope: the heat-current operator needs a proper justification or a qualified claim, and the chemical potential must be introduced for the arbitrary-filling statement. The referee report is based on the manuscript's internal consistency; the disagreement with prior work is not by itself a reason for rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Thanks for the report. I read the Rice-Mele paper carefully, and I think the reader's conditional verdict is close but actually too generous on the energy current. The missing piece is a real algebraic error, not a definitional preference.\n\nWhat's genuinely here: the finite-temperature charge transport formula, Eq. (17), is a clean extension of the zero-temperature Berry curvature result. The contour plot in Fig. 1 is useful for reading off ΔN for arbitrary circuits, and the argument that charge transport loses its quantization at finite temperature is correct. The paper is well-organized, and the charge part should survive review.\n\nThe problem is Eq. (5). The energy current derived from dH_m/dt has two commutator contributions: the on-site part gives -Δ J_p, but the hopping part gives a second-neighbor term -i v w (c†_{2m-1}c_{2m+1} - h.c.). That term is missing. You can see it directly from the commutator of the link hopping with the hopping inside H_m. In k-space it contributes E_n Ω_n, not Δ Ω_n. For the symmetric circuits (Δ0=0), Δ(t) is odd under t→T-t while Ω_n is even, so Δ Ω integrates to zero by symmetry. But E_n is even, so E_n Ω does not vanish generically. That kills the headline zero-heat result. The ∂H_m/∂t term does integrate to zero over a cycle, so it cannot rescue the claim.\n\nThe reader flagged this as a weak assumption; I'd call it a load-bearing flaw. The abstract and Section V both rest on Eq. (19), which is only valid if you define the energy current without the kinetic part. That is not the standard continuity-equation definition of heat current, and the paper does not justify it.\n\nBottom line: the charge-pumping part deserves a serious referee; the heat-pumping part needs major revision, or at least an explicit, physically motivated definition that excludes kinetic energy transport. I would send it to peer review because the claim is important and the error is subtle enough that a careful referee would catch it. But I would not cite the heat result as it stands.","headline":"Charge-pumping formulas are fine, but the zero-heat result is an artifact of a missing kinetic term in the energy current.","tokens_in":11138,"tokens_out":9256,"would_cite":false,"duration_ms":80453,"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":"For the non-interacting Rice-Mele chain, heat transported in a full pump cycle is not quantized, and for the common symmetric pump circuits it is exactly zero even where charge pumping remains quantized.","keywords":["Rice-Mele chain","charge pumping","heat transport","Berry curvature","Zak phase","finite temperature","adiabatic pumping","topological pump"],"falsifier":"Measure the energy transferred between two neighboring unit cells of an ultracold-atom Rice-Mele chain over one full symmetric elliptical pump cycle with $\\Delta_0=0$, $v_1=\\Delta_1=1$, $v_0=-1$: the paper predicts exactly zero net heat despite one unit of charge pumped, whereas the competing polarization-based picture of Ref. [34] predicts a nonzero, temperature-independent energy transfer; a direct calculation of the energy current that includes the explicit $\\partial H_m/\\partial t$ source term from the time-dependent parameters would also settle whether the vanishing-heat result survives once drive power is counted.","tokens_in":10126,"feed_emoji":"🔥","tokens_out":9125,"duration_ms":72607,"temperature":0.7,"pith_summary":"This paper works out the charge and heat carried across a link of the non-interacting Rice-Mele chain during an adiabatic pumping trajectory at arbitrary filling and temperature. The transported quantities are expressed as double integrals of analytic functions built from the Berry curvature and the Fermi occupation of the instantaneous bands. At zero temperature and half filling, charge transport remains quantized and topological, but heat transport is not: it is weighted by the instantaneous on-site energy inside the integral, and for the symmetric elliptical circuits commonly used in the literature the heat transported per full cycle is identically zero. At infinite temperature or for completely filled bands, all transported charge and heat vanish.","feed_headline":"Heat pumped per cycle is zero in common topological pump circuits","feed_subtitle":"In the Rice-Mele chain, heat transport is non-quantized and temperature-dependent, vanishing for symmetric pump cycles.","key_machinery":"The central object is the heat current operator for the non-interacting chain, $J_Q=-\\Delta\\,J_p$, obtained from the energy continuity equation, with $J_p$ the particle current operator across a link between unit cells (Eq. (5)). The argument is carried by writing the expectation value of $J_p$ as the Berry curvature $\\Omega_n(k,t)$ of the instantaneous Bloch bands (Eqs. (9)-(12)), so that the transported heat becomes the time integral of $\\Delta(t)$ times the rate of change of the Zak phase $\\gamma(t)$. The presence of $\\Delta(t)$ inside the time integral is what breaks the topological quantization of heat, and the oddness of $\\Delta(t)$ under $t\\to T-t$ for symmetric circuits is what makes the integrated heat vanish over a full cycle.","core_discovery":"The paper establishes that in the non-interacting Rice-Mele chain the heat transported through a link during an adiabatic process is, at half filling, $\\Delta Q(t)=-(1/2\\pi)\\int_0^t dt'\\,\\Delta(t')\\,\\partial\\gamma(t')/\\partial t'$, where $\\gamma$ is the Zak phase of the occupied band; the factor $\\Delta(t')$ inside the time integral prevents the heat per cycle from being a topological integer. Consequently, the number of particles pumped in a closed cycle is still the integer winding number of the Berry phase, while the heat pumped is a $\\Delta$-weighted winding that can vanish even when charge pumping is nontrivial. For any symmetric circuit with $\\Delta_0=0$ in the standard elliptical parametrization, the time-reversal symmetry $t\\to T-t$ of the integrand gives $\\Delta Q(T)=0$ at all temperatures, whereas more general circuits transfer heat between the even and odd sublattices and the environment. The paper provides the analytic double-integral formulas, Eqs. (12), (17), and (19), for the charge, energy, and heat currents, and shows numerically that temperature smooths the sharp topological transitions in the transported charge into crossovers.","pith_inferences":["Beyond the paper's claims, any circuit with $\\Delta(t)$ odd under $t\\to T-t$ should pump zero heat per cycle regardless of the trajectory shape, which would confirm the effect is a time-reversal symmetry property rather than a property of the chosen ellipse.","Beyond the paper's claims, these results imply that making a Thouless pump act as a heat engine requires breaking the time-reversal symmetry of $\\Delta(t)$; symmetric modulation, the most common experimental choice, drives no heat.","A testable extension is to evaluate the interacting heat current with the time-evolving block decimation method the paper proposes; if the same symmetric circuit still gives zero net heat at finite interaction, the vanishing result would be robust beyond free fermions.","The discrepancy with Ref. [34] may stem from what is counted as heat: the continuity-equation current used here excludes the energy exchanged directly with the external drive, and that excluded part could appear as 'heat' in polarization-based definitions."],"forward_implications":["For the standard symmetric elliptical pump circuits with $\\Delta_0=0$, the heat transported per full cycle is exactly zero at every temperature, even when the charge pumped is an integer.","For generic pump circuits with nonzero $\\Delta_0$, heat is transferred between the even and odd sublattices of the chain and the environment, with a magnitude that decreases as temperature rises and vanishes at infinite temperature.","The heat pumped per cycle is not a topological invariant; only the zero-temperature, half-filled charge transport is quantized.","At infinite temperature or for completely filled bands, all transported charge, energy, and heat vanish for any adiabatic trajectory.","Finite temperature converts the sharp topological transitions in the pumped charge, seen as a circuit is displaced in parameter space, into smooth crossovers that are relevant for ultracold-atom experiments with unavoidable heating."],"supporting_citations":[{"why":"Supplies the derivation that the particle current in the Rice-Mele chain equals the Berry curvature of the occupied band and the explicit form of the current operator used here.","marker":"[11]"},{"why":"The finite-temperature charge and energy pumping calculation for the Rice-Mele chain that this paper extends and challenges on the temperature and topological dependence of heat transport.","marker":"[34]"},{"why":"Establishes the quantization of charge transport over an adiabatic cycle, the topological baseline against which heat transport is compared.","marker":"[5]"},{"why":"Provides the Berry phase concept from which the Zak phase and Berry curvature used in the derivation are built.","marker":"[4]"},{"why":"Supplies the general formula for the Berry curvature of a two-band model used to obtain the explicit expression (12) for the Rice-Mele chain.","marker":"[44]"}],"fun_headline_variants":["Heat pumped per cycle is zero for common Rice-Mele circuits","In Rice-Mele, heat transport vanishes for symmetric pump cycles","Topological heat pumping fails in Rice-Mele at finite T","Charge pumps but heat doesn't in Rice-Mele symmetric cycles","Symmetric Rice-Mele pumps yield zero heat per cycle"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The results assume that the heat current in the driven chain is exactly the particle current times the instantaneous on-site energy, as obtained from an energy continuity equation that does not include an explicit term for the power delivered by the external drive that changes the parameters in time.","fun_headline_variants_meta":{"raw":{"variants":["Heat pumped per cycle is zero for common Rice-Mele circuits","In Rice-Mele, heat transport vanishes for symmetric pump cycles","Topological heat pumping fails in Rice-Mele at finite T","Charge pumps but heat doesn't in Rice-Mele symmetric cycles","Symmetric Rice-Mele pumps yield zero heat per cycle"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000854,"raw_usage":{"total_tokens":3707,"prompt_tokens":940,"completion_tokens":2767,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":556,"completion_tokens_details":{"reasoning_tokens":2682}},"tokens_in":556,"tokens_out":2767,"duration_ms":19818,"temperature":1.0,"reasoning_tokens":2682,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T13:49:34.767121+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the energy transferred between two neighboring unit cells of an ultracold-atom Rice-Mele chain over one full symmetric elliptical pump cycle with $\\Delta_0=0$, $v_1=\\Delta_1=1$, $v_0=-1$: the paper predicts exactly zero net heat despite one unit of charge pumped, whereas the competing polarization-based picture of Ref. [34] predicts a nonzero, temperature-independent energy transfer; a direct calculation of the energy current that includes the explicit $\\partial H_m/\\partial t$ source term from the time-dependent parameters would also settle whether the vanishing-heat result survives once drive power is counted.","supporting_citations":[{"cited_title":"Hattori , author K","cited_arxiv_id":null,"evidence_quote":"The finite-temperature charge and energy pumping calculation for the Rice-Mele chain that this paper extends and challenges on the temperature and topological dependence of heat transport."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Berry phase concept from which the Zak phase and Berry curvature used in the derivation are built."},{"cited_title":"Kordon , author J","cited_arxiv_id":null,"evidence_quote":"Supplies the general formula for the Berry curvature of a two-band model used to obtain the explicit expression (12) for the Rice-Mele chain."}],"review_version":1}