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arxiv: 2606.30465 · v1 · pith:KA4Z2YUHnew · submitted 2026-06-29 · ❄️ cond-mat.mes-hall

Heat rectification through a quantum two-level system

Tsuyoshi Yamamoto , Manuel Houzet This is my paper

Pith reviewed 2026-06-30 04:51 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords heat rectificationspin-boson modelKondo temperaturequantum two-level systemtensor networkOhmic bathsteady-state heat currentinfrared fixed point
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The pith

Heat rectification through an asymmetrically coupled quantum two-level system follows a universal power law near its infrared fixed point.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies steady-state heat flow in the Ohmic spin-boson model, where a two-level system couples asymmetrically to two thermal baths. It identifies a scaling regime around the Kondo temperature in which the system flows from an ultraviolet regime at higher temperatures to an infrared fixed point at lower temperatures. Perturbation theory applied near that infrared fixed point predicts that the rectification ratio obeys a universal power law, and tensor-network computations of the heat current confirm this prediction across the scaling window. The work shows how dissipation-induced correlations control thermal transport in a quantum impurity setting. A reader would care because the result supplies a concrete, parameter-free signature that links many-body physics to measurable heat rectification.

Core claim

The authors evaluate the steady-state heat current in the Ohmic spin-boson model with tensor networks and benchmark it against analytic limits. They locate a scaling regime that runs from the ultraviolet regime above the Kondo temperature to the infrared regime below it. Perturbation theory around the infrared fixed point then yields a universal power-law form for the rectification ratio, which the numerical data reproduce.

What carries the argument

Perturbation theory around the infrared fixed point of the Ohmic spin-boson model, which produces the universal power-law expression for the rectification ratio.

If this is right

  • The rectification ratio becomes independent of microscopic parameters once the system enters the infrared regime.
  • Tensor-network results match the analytic power-law prediction obtained from infrared perturbation theory.
  • Distinct transport regimes (weak coupling, incoherent tunneling, and strongly correlated scaling) produce qualitatively different rectification behavior.
  • Dissipation-induced many-body effects dominate the heat current once temperatures drop below the Kondo scale.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same infrared scaling might govern rectification in other quantum impurity models with bosonic baths.
  • Temperature-tuned measurements around the Kondo scale could serve as a diagnostic for the fixed-point structure in mesoscopic thermal devices.
  • The power-law form supplies a target signature for experiments that engineer asymmetric couplings in superconducting circuits or quantum dots.

Load-bearing premise

The tensor-network computation accurately captures the steady-state heat current throughout the scaling regime that flows from the ultraviolet to the infrared fixed point around the Kondo temperature.

What would settle it

A plot of rectification ratio versus temperature that deviates from the predicted power law in the regime below the Kondo temperature would falsify the central claim.

Figures

Figures reproduced from arXiv: 2606.30465 by Manuel Houzet, Tsuyoshi Yamamoto.

Figure 1
Figure 1. Figure 1: FIG. 1. Quantum heat transport through a two-level sys [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Schematic overview of the regimes considered in this [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Linear thermal conductance [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Heat rectification ratio [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Heat rectification ratio [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. MPO representation of the transfer matrix [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Time evolution of the correlation function [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
read the original abstract

We study heat rectification through a quantum two-level system asymmetrically coupled to two thermal baths, as described by the Ohmic spin-boson model. We evaluate the steady-state heat current using a tensor-network approach, which enables us to access the strongly correlated regime, and benchmark the results against analytical formulas in several limiting regimes, including the weak-coupling and incoherent-tunneling regimes. We identify a scaling regime where the studied system flows from an ultraviolet regime, at temperatures larger than the Kondo temperature, to an infrared regime, at temperatures lower than the Kondo temperature. By applying perturbation theory near the infrared fixed point, we find that the rectification ratio follows a universal power law. Our numerical results agree well with this analytical prediction. Our results provide a fundamental understanding of how dissipation-induced many-body physics affects heat transport.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper examines heat rectification in the Ohmic spin-boson model with asymmetric bath couplings. Tensor-network methods are used to compute the steady-state heat current in the strongly correlated regime, with benchmarks against analytic limits in weak-coupling and incoherent-tunneling regimes. A scaling regime is identified flowing from UV (T ≫ TK) to IR (T ≪ TK) fixed points around the Kondo temperature. Perturbation theory near the IR fixed point yields a universal power law for the rectification ratio, with reported numerical agreement.

Significance. If the tensor-network results reliably capture the scaling window, the work provides a concrete link between many-body Kondo physics and heat rectification, with potential implications for quantum thermal devices. The combination of an analytic power-law derivation (independent of fitting) and numerical validation is a positive feature.

major comments (1)
  1. [Numerical methods / tensor-network section (as described in abstract)] The central claim of numerical agreement with the analytic power law rests on the tensor-network method accurately extracting the steady-state heat current throughout the UV-to-IR scaling regime around TK. The abstract positions this method as essential for the strongly correlated regime, yet no explicit convergence tests, truncation-error bounds, or comparisons to known limits inside the scaling window are referenced in the provided description; this leaves the validation inconclusive.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on the numerical validation. We address the single major comment below.

read point-by-point responses

  1. Referee: [Numerical methods / tensor-network section (as described in abstract)] The central claim of numerical agreement with the analytic power law rests on the tensor-network method accurately extracting the steady-state heat current throughout the UV-to-IR scaling regime around TK. The abstract positions this method as essential for the strongly correlated regime, yet no explicit convergence tests, truncation-error bounds, or comparisons to known limits inside the scaling window are referenced in the provided description; this leaves the validation inconclusive.

    Authors: We agree that the abstract (and the summary description) does not explicitly reference convergence tests, truncation-error bounds, or direct comparisons inside the scaling window, which leaves the validation of the central claim less conclusive than it could be. The manuscript does benchmark the tensor-network results against analytic formulas in the weak-coupling and incoherent-tunneling regimes, but these lie outside the strongly correlated scaling regime of interest. To strengthen the paper, we will add an appendix (or expanded methods section) that reports explicit convergence tests with respect to bond dimension and time-step, truncation-error estimates, and additional comparisons to known limits or perturbative results inside the UV-to-IR window around TK. This revision will directly address the concern and make the numerical support for the universal power law more robust. revision: yes

Circularity Check

0 steps flagged

Analytical perturbation theory yields independent power-law prediction

full rationale

The paper derives the universal power-law rectification ratio via perturbation theory applied near the infrared fixed point of the Ohmic spin-boson model. This analytical step is performed after identifying the UV-to-IR scaling regime around the Kondo temperature and is benchmarked against separate limiting-case formulas (weak-coupling, incoherent tunneling). The tensor-network numerics are used only for validation in the strongly correlated regime and do not enter the derivation of the power law itself. No self-citations, fitted parameters renamed as predictions, or self-definitional steps are present in the reported chain; the central claim therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the Ohmic spin-boson model with asymmetric bath coupling, the accuracy of the tensor-network method in the strongly correlated regime, and the validity of perturbation theory around the infrared fixed point. No explicit free parameters are identified in the abstract as being fitted to data; the Kondo temperature functions as a crossover scale rather than a fitted constant. No new entities are postulated.

axioms (2)
  • domain assumption The Ohmic spin-boson model with asymmetric coupling to two baths describes the essential physics of the heat-rectifying two-level system.
    Invoked at the outset of the abstract as the model under study.
  • domain assumption The tensor-network method yields the correct steady-state heat current in the strongly correlated regime.
    Required for the numerical results that are then compared to the analytic power law.

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Reference graph

Works this paper leans on

69 extracted references · 2 canonical work pages

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    = ∆/π(see Eq. (23)). While the leading contributionJ 2 does not induce heat rectification, the next-leading contributionJ (a) 4 can give rise to rectification, since it originates from the anhar- monic term∝˜ρ 4 in Eq. (32b). By contrast, the contri- butionJ (b) 4 does not induce rectification either, because it comes from a harmonic term in the field∝˜ρ∂...

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    Feynman-Vernon path integral First, we show the real-time dynamics of the two-level system using the Feynman-Vernon path-integral formal- ism [44]. The time-evolution of the reduced density ma- trix of the two-level system,ρ(t) = tr B[ϱ(t)], whereϱ(t) is the density matrix of the global system and tr B[O] de- notes tracing over with respect to the degree ...

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    To overcome this, we adopt the tensor network algorithm, the time-evolving matrix product operators (TEMPO) [43]

    TEMPO The memory effects caused by the coupling to the bath prevent us from computing the long-time dynam- ics. To overcome this, we adopt the tensor network algorithm, the time-evolving matrix product operators (TEMPO) [43]. Introducing the augmented density tensor (ADT) Ay0,...,yM = MY m≤n=0 F yn,ym[ρ]y0 ,(A7) whereF yn,ym is the renormalized influence ...

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    Steady-state heat current The steady-state heat current (14) is rewritten as J= αLαR α Z ∞ 0 dt χ(t)[F(t, T L)−F(t, T R)],(A17) whereF(t, T r) is the window function F(t, T r) = Z ∞ 0 dω ω 2e−ω/ωc sin(ωt)nr(ω) =T 3 r Im h ψ(2)(1 + (it+ω −1 c )Tr) i ,(A18) whereψ (2)(z) =d 2ψ(z)/dz 2 is the polygamma func- tion of order 2, and it decays asF(t, T L)−F(t, T ...

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    ContributionJ 2 The commutation [H L 0 , V2] is [H0 L, V2] =−ig 2[α1(:ρ L ˙ρL : + : ˙ρLρL :) + 2√αLαR : ˙ρLρR :],(B6) where we writeρ r = ˜ρr(x= 0) for simplicity and g2 =πc 2TK/α(v/TK)2. Noting that, for the free bosonic Hamiltonian, the different modes are separable, ⟨OLOR⟩0 =⟨O L⟩L ⟨OR⟩R and the odd-order moments are zero,⟨ρ 2n+1 r ⟩r = 0, the steady-s...

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    ContributionJ (a) 4 The steady-state heat currentJ (a) 4 is obtained, in the same manner asJ 2, as J(a) 4 =−8ig 2g4αLαR × Z ∞ −∞ dt n αL ⟨[: ˙ρL(0)ρR(0) :,:ρ 3 L(t)ρR(t) :]⟩0 +α R ⟨[: ˙ρL(0)ρR(0) :,:ρ L(t)ρ3 R(t) :]⟩0 = 24ig2g4αLαR(αL ⟨:ρ 2 L :⟩L +α R ⟨:ρ 2 R :⟩R) × Z ∞ −∞ dt h ˙¯SL(t) ¯SR(t)− ˙SL(t)SR(t) i = 48g2g4αLαR(αL ⟨:ρ 2 L :⟩L +α R ⟨:ρ 2 R :⟩R) × ...

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    In the Fourier space, it reads J(b) 4 =−4g 2g3αLαR × Z ∞ −∞ dω 2π ω n SL(ω)DR(−ω)−D L(−ω)SR(ω) o , (B13) where we used ¯Dr(ω) =D r(−ω)

    ContributionJ (b) 4 The contribution fromV (b) 4 is calculated as J(b) 4 =−2ig 2g3αLαR × Z ∞ −∞ dt n ⟨[: ˙ρL(0)ρR(0) :,;ρ L(t)∂2 xρR(t) :]⟩0 +⟨[: ˙ρL(0)ρR(0) :,:∂ 2 xρL(t)ρR(t) :]⟩0 =−2ig 2g3αL X r αr Z ∞ −∞ dt[ ˙SL(t)Dr(t) + ˙DL(t)Sr(t) − ˙¯SL(t) ¯Dr(t)− ˙¯DL(t) ¯Sr(t)], (B12) withg 3 =−πc 4TK/(2α)(v/TK)4 and the correla- tion functions,D r(t) =⟨∂ 2 xρr(...

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    Spectral function Now, we calculate the spectral functionA r(ω). The bosonic fields in the free bosonic Hamiltonian at the IR fixed point with the lengthLare expressed as ˜ϕr(x) = X n>0 r π knL cos(knx)(akn +a † kn ),(B15a) ˜ρr(x) = X n>0 1 i r kn πL cos(knx)(akn −a † kn ),(B15b) wherek n =nπ/L. Hence, using these fields, the spectral function is Ar(ω) = ...

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    Fluctuations The auto-correlation function of ˜ρr(x= 0) =ρ r at the same time is, using the spectral function (B16), ⟨ρ2 r⟩=S r(t= 0) = Z ∞ −∞ dω 2π Ar(ω) 1−e −ω/Tr = 1 (πv)2 Z ∞ 0 dω ω[2n r(ω) + 1].(B17) Therefore, we obtain the fluctuations ofρ r as ⟨: ˜ρ2 r(x= 0) :⟩= T 3 3v2 .(B18) By plugging the spectral function (B16) and the fluc- tuations (B18) in...

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