Controlled Buildup of Half-Quantized Thermal Conductance in an Engineered Chiral Spin Liquid Platform

Baptiste Bermond; Bo-Ye Sun; Lucila Peralta Gavensky; Marin Bukov; Nathan Goldman; Zheng-Wei Zhou

REVIEW 3 major objections 5 minor 67 references

Controlled Buildup of Half-Quantized Thermal Conductance in an Engineered Chiral Spin Liquid Platform

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read A small, finite Kitaev channel coupled to two Ising chains reaches the half-quantized thermal conductance $\pi/12$ in a quasi-steady time window.

desk verdict Serious proposal, but the half-quantized claim is made inside a vortex-free sector that the tunnel coupling itself can leave; referee time is warranted. read the letter →

arxiv 2509.03355 v1 pith:ZAPDUQZ2 submitted 2025-09-03 cond-mat.quant-gas cond-mat.mes-hallcond-mat.othercond-mat.str-elquant-ph

Bo-Ye Sun , Baptiste Bermond , Lucila Peralta Gavensky , Marin Bukov , Zheng-Wei Zhou , Nathan Goldman This is my paper · ORCID

classification cond-mat.quant-gascond-mat.mes-hallcond-mat.othercond-mat.str-elquant-ph

keywords half-quantizedthermalconductancechiralspinliquidKitaevhoneycombmodelMajoranaedgemodesLandauer-Büttikertransporttransverse-fieldIsingreservoirsfinite-sizeeffectscold-atomquantumsimulator

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to show that the half-quantized thermal conductance, a hallmark of Majorana edge transport, can be observed in a small and finite Kitaev honeycomb channel rather than only in idealized infinite systems. The proposed device connects the chiral spin liquid to two one-dimensional transverse-field Ising chains held at different temperatures; after an adiabatic ramp of the tunnel couplings, the heat current develops a quasi-steady window in which $\kappa/T$ approaches $\pi/12$. To isolate the physical signal, the authors take half the difference of the two reservoir currents, which cancels a symmetric ground-state contribution that otherwise masks the plateau, and they verify the same result with a Landauer-Büttiker transmission calculation for long reservoirs. The payoff is a concrete measurement protocol for detecting a topological thermal signature in engineered cold-atom or Rydberg settings, where reservoirs are necessarily finite.

What carries the argument

The load-bearing object is the excitation-only conductance extraction $\kappa/T = |(J_l^E-J_r^E)/(T_l^2-T_r^2)|$ [Eq. (12)], which uses the equality of the two reservoirs' ground-state currents to cancel their spurious contribution and leaves only quasiparticle heat transport. The underlying representation is a global Majorana-fermion rewriting of the channel, reservoirs, and tunnel couplings, in which the thermal current is a reservoir-channel spin correlation and the zero-energy Majorana mode enforces $T(\omega)\to 1$ as $\omega\to 0$. A simplified four-state model of the two lowest channel levels explains the transmission plateau: its width is set by the level spacing $\epsilon$, and the optimal coupling corresponds to $\epsilon = 2\sqrt{A_0A_1}$, which is why tuning $J_T$ to $0.8J_0$ or $0.6J_0$ according to the magnetic field produces the flattest plateau and the cleanest half-quantization.

What would settle it

Recompute the thermal conductance of the $8\times 4$ channel at $T_l=0.024J_0$ without restricting to the vortex-free sector, for example by sampling vortex configurations or including the vison sector; if the extracted $\kappa/T$ moves away from $\pi/12$ by more than the fitting uncertainty of Fig. 6, the high-temperature plateau claim fails. Alternatively, a cold-atom or Rydberg realization that measures the reservoir-channel correlator in Eq. (6) could directly confirm or rule out the plateau in the predicted time window.

Watch

Extended reading notes

Core claim

The central claim is that a finite chiral spin liquid, modeled as an $8\times 16$ cylindrical Kitaev lattice, can mediate two-terminal heat transport with conductance saturating at $\kappa/T=\pi/12$ once the reservoir-channel coupling is tuned to an optimal strength $J_T^*\approx 0.8J_0$ at low temperature. The half-quantization is traced to the topologically protected zero-energy Majorana mode: particle-hole symmetry forces the transmission rate $T(\omega)$ to unity as $\omega\to 0$, and the low-temperature Fermi window samples only that region. In a finite system, discrete level spacing and coupling-induced broadening compete; the optimal coupling merges the lowest levels into a near-unit transmission plateau, while lowering the temperature or reducing the channel's circumference widens the parameter window over which the plateau value survives. The paper also argues that taking half the difference of the two reservoir currents yields a stable conductance in the quasi-steady window, and that the Landauer-Büttiker formula agrees with direct time evolution when the reservoirs are sufficiently long.

Load-bearing premise

The entire calculation assumes the Kitaev channel stays in its vortex-free sector (all flux variables $\eta_b=1$), which is justified only at very low temperature; the higher-temperature plateau at $T_l=0.024J_0$ could be altered by vortex excitations that the paper explicitly leaves out of scope.

Editorial extensions

If this is right

A two-terminal heat measurement on a finite engineered Kitaev channel can read out the half-quantized conductance in a quasi-steady time window, without requiring infinite reservoirs or a true long-time steady state.
Tuning the tunnel coupling $J_T$ to the value that maximizes the near-unit transmission plateau is a practical control knob; the same Landauer-Büttiker calculation that predicts the plateau also predicts the optimal $J_T$ for a given magnetic field.
Reducing the periodic circumference to four unit cells enlarges the level spacing and shifts the half-quantized plateau up to $T_l=0.024J_0$, more than an order of magnitude above the ultralow-temperature regime needed for larger circumferences.
As the system grows along the periodic direction, the discrete transmission valleys fill in, so the finite-size plateau continuously connects to the conventional chiral-edge picture of half-quantized thermal Hall transport.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

I would expect the half-difference current subtraction to transfer directly to other Majorana transport platforms with symmetric identical leads: it removes contact ground-state heating without needing a Kubo or steady-state assumption.
The few-state condition $\epsilon = 2\sqrt{A_0A_1}$ suggests a possible finite-size engineering rule: choose the channel circumference so that the first excited level spacing matches the coupling-induced broadening, which would let one tune the plateau width without changing the magnetic field.
The high-temperature plateau of Fig. 6 is the part most exposed to the vortex-free assumption; including vison excitations at $T_l=0.024J_0$ in the same geometry would show whether the plateau survives or where it breaks.
One could also test the plateau experimentally by replacing the thermal reservoirs with synthetic heat baths and measuring the reservoir-channel spin correlation $\langle S^y_l S^x_{C_l}\rangle$ directly, since Eq. (6) identifies this correlator as the current.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear X,

The thing to know: this is a serious, readable proposal for seeing half-quantized thermal conductance in a cold-atom/Rydberg Kitaev simulator, but the headline result is computed in a vortex-free sector that the coupling Hamiltonian itself can leave. Until that truncation is controlled, the claim is conditional.

What is genuinely new is the dynamical protocol—adiabatic ramp, finite reservoirs, quasi-steady window—and the clean way they extract the excitation conductance by half-differencing left/right currents [Eq. (12)]. The Landauer-Büttiker agreement in Fig. 3(d) is a real internal consistency check, not a fit, and the paper is unusually honest about its assumptions and gives concrete parameters for a Rydberg implementation. That part deserves credit.

The soft spot is the vortex-free projection. The tunnel term HT in Eq. (3) contains S^x on a channel site, which in the exact Kitaev model has matrix elements between different flux sectors. The paper justifies the vortex-free restriction by citing Nasu et al. on thermal vison proliferation below 0.01J0, but that addresses the initial Gibbs state, not the dynamics. The relevant small parameter is the ratio of the vison-creation matrix element to the vison gap, roughly J_T/Δ_vis, and with J_T ~0.8–1.2J0 and Δ_vis ~0.02–0.06J0 that ratio is not small. Both the time evolution and the Landauer-Büttiker calculation use the same projected Hamiltonian, so their mutual agreement cannot detect the missing process, and no estimate of flux-changing matrix elements is given. This is not just a Fig. 6 issue; it touches the low-temperature claims in Figs. 3 and 5. A perturbative bound or a calculation including one vison sector would settle it.

Weaker points: the plateau windows in Fig. 3 are visually selected (they include error bars, so this is minor), and the toy model in App. F leans on A0≈A1 without quantifying the approximation. No code or data is shipped, which limits reproducibility. The citation pattern looks fair; the authors cite the relevant exact-solution, QMC, and transport literature, and the self-citations to their own Kitaev engineering work are appropriate.

Who gets value: people working on engineered Kitaev simulators, Majorana thermal transport, or finite-bath nonequilibrium methods should read it. I would send it to a serious referee, not desk reject; the vortex question is exactly the kind of thing a good referee can push to a quantitative answer. I would not cite it as evidence for half-quantized conductance until that answer exists.

Best, [You]

Referee Report

3 major / 5 minor

Summary. The paper proposes a two-terminal thermal transport setup in which a finite chiral spin liquid (Kitaev honeycomb model with a magnetic field, on a cylinder) is coupled at two edge points to transverse-field Ising chain reservoirs. A protocol adiabatically ramps the tunnel couplings, and the thermal current is extracted from spin correlations at the contacts. The central claim is that, after subtracting the ground-state contribution, the quasi-steady thermal conductance approaches the half-quantized value π/12 over a finite time window, for optimal coupling and ultralow temperatures. The authors support this with direct time-evolution simulations restricted to the vortex-free Majorana sector and with a Landauer-Büttiker formula derived from the same projected Hamiltonian; they show agreement between the two methods for sufficiently long reservoirs. They also analyze the dependence of the conductance on coupling strength, magnetic field, temperature, and finite-size effects, and provide a toy model for the transmission plateau.

Significance. If the central claim holds, the paper provides a concrete and experimentally plausible route to observing half-quantized thermal conductance in engineered cold-atom or Rydberg-atom simulators, with estimated measurement times on the order of 100–150 μs. The strengths of the manuscript are substantial: the time-evolution calculations are exact within the vortex-free sector; the Landauer-Büttiker derivation in Appendix C explicitly accounts for the number-non-conserving Majorana couplings and yields a parameter-free prediction of the half-quantized value; the finite-size Chern number check in Appendix H supports the topological interpretation; and the analytic toy model in Appendices F and G explains the transmission plateau and its stability. The agreement between direct evolution and the Landauer-Büttiker formula in Fig. 3(d) is a genuine cross-check, albeit within the same projected model. The main risk is the uncontrolled vortex-free truncation under strong reservoir coupling, which affects the physical validity of the central claim.

major comments (3)

[Sec. II.C and App. A (after Eq. A8; Eq. A9)] The entire calculation restricts the Kitaev channel to the vortex-free sector (all η_b = 1), justified by the temperature being below 0.01 J_0 with a citation to Nasu et al. That argument addresses the initial equilibrium state, not the subsequent dynamics. The tunnel coupling H_T in Eq. (3), written in Majorana form in Eq. (A9) as iJ_T/4 (c-bar_l c_{Cl} + c-bar_r c_{Cr}) with all η_b set to 1, drops the flux-changing matrix elements of the original spin exchange term S^x_l S^x_{Cl}. In the exact Kitaev model, this spin operator can flip the conserved fluxes η_b, and the relevant small parameter is not T/(0.01J_0) but the ratio of the vison-creation matrix element to the vison gap, roughly J_T/Δ_vis. Since the optimal couplings used in Figs. 4–6 are J_T = 0.6–1.2 J_0, and vison gaps in the Kitaev model are typically of order 0.02–0.06 J_0, this ratio is not small. Vison creation at the contacts could substantially modify the heat current even at the ultralow temperatures of Figs. 3 and 5. Because both the time-evolution simulation and the Landauer-Büttiker formula use the same projected Hamiltonian, they cannot detect this error. The paper needs to quantify the flux-changing matrix elements of H_T, or provide an independent check (e.g., exact diagonalization of a small full Kitaev model with reservoirs) establishing that vison creation is negligible in the parameter regime of the central claim.
[Sec. IV.B, Fig. 6 and Sec. II.C] The higher-temperature plateau in Fig. 6(b) uses T_l = 0.024 J_0, which exceeds the paper's own quoted vortex-free validity threshold (T < 0.01 J_0, Sec. II.C). The manuscript explicitly states that vortex-related effects are beyond the scope of the work. This is a load-bearing limitation: Fig. 6 is presented as a practical route to observe half-quantized conductance under less extreme cooling, but if vison proliferation contributes substantially to heat transport at 0.024 J_0, the plateau in Fig. 6(b) could be materially altered. The authors should either restrict the claim to temperatures below the quoted threshold, or provide an estimate of the vison contribution at the parameters of Fig. 6.
[Sec. III.A.1, Eq. (12) and Fig. 3(b)] The extraction of the excitation thermal conductance in Eq. (12) as half the difference of the two reservoir currents assumes that the ground-state contributions to J_l^E and J_r^E are exactly equal and therefore cancel. The paper demonstrates this cancellation for one parameter set through the overlapping black curves in Fig. 3(b), but it does not verify the cancellation across the parameter ranges used in Figs. 5 and 6, where the magnetic field and the coupling strength are varied. In a finite chiral system, the two contacts are not necessarily equivalent under reflection if the chiral edge current breaks the relevant symmetry, and unequal ground-state leakage would bias the extracted κ/T. The paper should provide a quantitative check, for example comparing Eq. (12) with the excitation-only result (the orange curve in Fig. 3(b)) for the parameters used in the main figures, or reporting the residual T=0 difference |J_l^0 - J_r^0| over the h–J_T parameter plane.

minor comments (5)

[Fig. 3 caption and Sec. III.A.2] In Fig. 3(d), the text refers to the Landauer-Büttiker curve as red and the direct-evolution curve for 200 reservoir sites as blue, but the caption only mentions the blue curve as showing strong agreement. Adding a color key directly in the caption would improve readability.
[Eq. (7) and App. B, Eq. (B8)] The density matrix formula in Eq. (7) contains a factor 2 and a ground-state term (last term) whose physical interpretation is explained only later in the text. A short sentence immediately after Eq. (7) identifying the last term as the zero-temperature contribution would help readers follow the subtraction procedure.
[App. B, Eq. (B1) and Eq. (A10)] The notation Q(t) = e^{-tA} is confusing, since the Hamiltonian in Eq. (A10) is defined as H = i/4 Σ A_{jj'} c_j c_{j'}; the time-evolution operator in the Majorana adjoint representation is not simply e^{-tA} as written. The authors should clarify the relationship between the matrix A and the orthogonal time-evolution matrix used in the computation.
[App. F, Eqs. (F2)–(F3)] The toy model introduces phenomenological parameters A_0, A_1, A_2 and later imposes A_2^2 ∼ A_0 A_1 and 4A_0^2 = ε^2 to obtain the flat transmission plateau. The connection of these conditions to the actual microscopic parameters (J_T, h, system size) is not derived; stating explicitly that these are fitting parameters used only for qualitative insight would avoid over-interpretation.
[App. D, Fig. 7] The caption of Fig. 7 says 'T_l is always set to be 0.006 J_0', which is incompatible with the ratio T_l = 1.2 T_r shown in the legend; if T_l is fixed, then T_r varies between the two cases. The wording should be corrected to specify which temperature is held fixed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the half-quantized conductance is a computed outcome, and the Landauer-Büttiker agreement is a consistency check rather than a fitted or self-referential input.

full rationale

The derivation chain is self-contained. The central observable κ/T in Eq. (12) is extracted from time-evolved reservoir currents as half the difference of the two currents; this is a measurement prescription designed to cancel equal ground-state contributions, not a fit to the half-quantized target. The Landauer-Büttiker expression Eq. (9) is re-derived in App. C from the same projected Majorana Hamiltonian, so the agreement in Fig. 3(d) is a consistency check between the LB approximation and the time evolution, not an independent empirical confirmation; the paper presents it as such. The half-quantized value π/12 is obtained analytically by setting T(ω)=1 in Eq. (9), but the actual T(ω) is computed from the model, and Figs. 4–6 show conductance deviating from half-quantization away from optimal parameters, so the result is not forced by construction. The vortex-free sector restriction (all η_b=1) is an approximation justified by citing Nasu et al. for low-temperature vison suppression; whether HT can create visons dynamically is an accuracy or truncation concern, not a circularity. Self-citations ([10], [57], [59]) provide derivations or standard techniques rather than a load-bearing uniqueness claim. No circular step can be quoted from the manuscript.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced. The free parameters are the reservoir field choice, the optimal coupling read off from spectra, and the toy-model amplitudes. The main load-bearing assumption is the vortex-free sector, which is plausible at the low temperatures used in most of the paper but questionable at the higher temperature 0.024 J0 used in Fig. 6.

free parameters (3)

reservoir field B = JR/2 = B = JR/2
Chosen, as stated in Sec. II A, so that the Ising reservoir spectrum in Eq. (A7) is gapless. This is a tuning condition for the reservoir, not fitted to the target result, but it is an input choice that the central claim depends on.
optimal coupling J*_T = 0.8 J0 for h = 0.1 J0; 0.6 J0 for h = 0.05 J0; 1.2 J0 for 8x4y at h = 0.1 J0
The key control parameter. The value is read off the transmission spectra in Fig. 4 and the conductance curves in Figs. 5 and 6. The toy model in App. F explains the condition epsilon = 2 sqrt(A0 A1), but the explicit value of J*_T is obtained numerically from the simulations, not predicted from first principles.
A0, A1, A2 amplitudes in the toy model = Not given numerical values; constrained only by symmetry and scaling with J_T^2
In App. F, the transmission plateau is explained by a phenomenological self-energy with amplitudes A0, A1, A2. The condition A0 = A1 is an additional assumption justified only by approximate equality of boundary wavefunctions. These are fitting parameters used to reproduce the plateau shape, not derived from the underlying Hamiltonian.

assumptions (4)

domain assumption The Kitaev channel stays in the vortex-free sector, eta_b = 1 for all bonds.
Invoked in App. A after Eq. (A8) and used throughout. Justified by very low temperature and the cited quantum Monte Carlo result of Nasu et al. [24]. This is a physical restriction that excludes vortex sectors from the entire calculation.
domain assumption The reservoirs are large enough that their Green functions remain unchanged, so the Landauer-Büttiker steady-state derivation applies.
Stated in Sec. II C 2, App. C, and again in Sec. III A 2. The paper verifies this numerically in Fig. 3(d) by comparing with time evolution, so it is a numerically supported assumption, but it is still a background assumption of the derivation.
domain assumption The reservoir spectrum is gapless because B = JR/2 (Eq. A7).
This guarantees low-energy modes in the reservoirs at low temperature. The paper states this in Sec. II A and App. A. It is a deliberate model choice.
domain assumption In App. F, the number-non-conserving terms in the coupling are the reason for the off-diagonal Gamma entries; without them transmission near zero deviates from unity.
The paper verifies this in a modified toy model (Fig. 10), so it is a numerically supported modeling assumption within the toy model, but the toy model itself uses the phenomenological Gamma of Eqs. (F2) and (F3).

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Pith. "Pith review of Controlled Buildup of Half-Quantized Thermal Conductance in an Engineered Chiral Spin Liquid Platform." pith.science (2026). https://pith.science/paper/ZAPDUQZ2

@misc{pith2026250903355,
  author       = {Pith},
  title        = {Pith review of: Controlled Buildup of Half-Quantized Thermal Conductance in an Engineered Chiral Spin Liquid Platform},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZAPDUQZ2}},
  note         = {Machine review of arXiv:2509.03355}
}

read the original abstract

We study thermal transport along the edge of a small chiral-spin-liquid device coupled to two Ising-chain reservoirs, a platform suitable for quantum-engineered systems. Adiabatically switching on the tunnel couplings to the reservoirs generates a thermal current that dynamically builds up and reaches a quasi-steady-state regime. In this time window, the two-terminal thermal conductance can approach half-quantized values -- a hallmark of Majorana-mediated transport -- under finely tuned conditions. The results agree with a steady-state Landauer-B\"uttiker description for sufficiently large reservoirs, where energy-resolved transmission rates help identify the optimal parameters to achieve the half-quantized conductance. This work provides a controllable platform to investigate topological thermal transport in engineered spin systems, such as realized in cold-atom and Rydberg-atom settings.

Figures

Figures reproduced from arXiv: 2509.03355 by the authors.

**Figure 1.** Schematic of the proposed system. The chiral spin liquid (red and blue sites) is coupled to two reservoirs (yellow sites) along the same edge. Each reservoir is modeled as a one-dimensional transverse-field Ising chain with open boundary conditions, and ⊙ denotes the local transverse fields acting on the Ising spins. The green (x), pink (y), and purple (z) bonds indicate the direction α of the bonds ⟨i, j⟩α in the … view at source ↗

**Figure 2.** Structure of the system used in numerical calculation. (a) The overall configuration of the system, and (b) its enlarged view. The central channel, a cylindrical chiral spin liquid, has open boundaries in the x direction and periodic boundaries along y. The two reservoirs (yellow sites), each formed by a one-dimensional transverse-field Ising model with open boundaries, connect to the channel at diametrically oppo… view at source ↗

**Figure 4.** (c) shows T (ω) for h = 0.1J0 at various JT . In the weak coupling regime (JT = 0.6J0, red curve), Γ l/r is appreciably smaller than the energy level spacing, and the transmission spectrum features well-separated sharp peaks that align with the discrete eigenvalues of the channel shown by the yellow lines in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

Figures from the paper (6 more)

**Figure 6.** Figure 6: Transmission rate and thermal conductance with four unit cells along the periodic direction. (a) Transmission rate vs. frequency under different coupling strengths at h = 0.1J0. With a limited number of sites, the large energy spacing between the lowest states results…

**Figure 8.** Figure 8: Magnetic field dependence of the bulk gap in the finite chiral spin liquid channel for different lengths along the ydirection. The x and y denote the number of unit cells along the x and y-direction, respectively. Due to finite-size effects, the bulk gap remains fini…

**Figure 7.** Figure 7: Robustness against reservoir temperature imbalance. (a) and (b) Coupling strength JT /J0 and magnetic field strength h/J0 dependence of thermal conductance at different temperature ratios Tl/Tr, respectively. Thermal conductance remains stable across different tempera…

**Figure 9.** Figure 9: Comparison of transmission rates between the simplified and full models under varying coupling strengths at h = 0.1J0. The green, blue, and red dashed curves indicate the transmission rate from the full model, while solid curves represent the simplified model, consid…

**Figure 10.** Figure 10: Influence of the number-non-conserving (NNC) terms from the Majorana nature of the system. Dashed curves show the transmission with all interactions included, while solid curves exclude the number-non-conserving terms (NNC, as marked in the figure). The absence of NNC…

**Figure 11.** Figure 11: Influence of larger Ly (a)-(d) Transmission spectrum for Ly = 16 (red curve) and Ly = 80 (blue curve) under different h and JT . In the gap region, dense peaks corresponding to the chiral edge states appear when Ly is large. The orange curve is the normalized energy …

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Works this paper leans on

67 extracted references · 54 canonical work pages

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II B, the reservoirs are initially decou- pled from the central channel, and each is prepared in thermal equilibrium at a known temperature

Direct time-evolution simulation As described in Sec. II B, the reservoirs are initially decou- pled from the central channel, and each is prepared in thermal equilibrium at a known temperature. Under this condition, the excitations in both the reservoirs and the channel follow the Fermi distribution. This allows us to construct the initial density matrix...

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(A8) and (A6)]

Landauer-Büttiker formula approach In our system, both the Kitaev model and the transverse- field Ising model can be reformulated in terms of Majorana fermions [see Eqs. (A8) and (A6)]. However, when expressed in their respective eigenstate representations, the tunneling Hamiltonian involves processes that do not conserve the num- ber of quasiparticles. T...

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Res 100" and

Thermal conductance from direct time evolution simulation As introduced in the previous section, the time evolution of the quasi-thermal conductanceκl/r/T [see Eq. (8)] can be obtained numerically and the result after the ramping, i.e., for t >10ts = 200J0, is shown in Fig. 3(a). The curves in dif- ferent colors correspond to different reservoir lengths, ...

work page
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(12), the system can also be analyzed using the Landauer- Büttiker formula; see Refs

Comparison with the Landauer-Büttiker formalism Beyond the direct time-evolution calculations based on Eq. (12), the system can also be analyzed using the Landauer- Büttiker formula; see Refs. [51–53] for previous applications to Majorana-related transport problems. Using Eq. (11), we evaluate the thermal conductance from the Landauer-Büttiker formula and...

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Influence of coupling strength To systematically explore different transport regimes, we analyze the transmission spectrumT (ω) by varying the cou- pling strength JT . The interplay between the broadening Γl/r∝J2 T and the discrete energy level structure of the finite- sized channel leads to qualitatively distinct behaviors, depend- ing on whether Γl/r is...

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(9)], the thermal conductance is obtained by integrating T (ω) against the difference in occupation functions

Influence of temperature According to the Landauer-Büttiker formalism [Eq. (9)], the thermal conductance is obtained by integrating T (ω) against the difference in occupation functions. In particu- lar, by setting T (ω) = 1 in Eq. (9), one obtains the result κ/T = π/12 (in natural units with kB = ℏ = 1), which cor- responds to the half-quantized value [24...

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Dependence on coupling strength, magnetic field, and temperature Building on the understanding established via the Landauer-Büttiker analysis, we now examine the thermal con- ductance calculated from the direct time-evolution calculation (see Sec. II C 1). As shown in Fig. 5(a) with h = 0.1J0, which is the same field used in Fig. 4(c), the conductance dep...

work page
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Specifically, we find that the half- quantized thermal conductance can emerge at higher temper- atures when the coupling strength is appropriately tuned

Enhancing quantized conductance at higher temperatures via finite-size effects While our earlier analysis emphasized the necessity of ul- tralow temperatures for observing half-quantized thermal con- ductance, primarily due to finite-size-induced suppression of transmission away from ω = 0, a notable exception emerges under special conditions. Specificall...

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

II B, the reservoirs are initially decou- pled from the central channel, and each is prepared in thermal equilibrium at a known temperature

Direct time-evolution simulation As described in Sec. II B, the reservoirs are initially decou- pled from the central channel, and each is prepared in thermal equilibrium at a known temperature. Under this condition, the excitations in both the reservoirs and the channel follow the Fermi distribution. This allows us to construct the initial density matrix...

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[2] [2]

(A8) and (A6)]

Landauer-Büttiker formula approach In our system, both the Kitaev model and the transverse- field Ising model can be reformulated in terms of Majorana fermions [see Eqs. (A8) and (A6)]. However, when expressed in their respective eigenstate representations, the tunneling Hamiltonian involves processes that do not conserve the num- ber of quasiparticles. T...

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[3] [3]

Res 100" and

Thermal conductance from direct time evolution simulation As introduced in the previous section, the time evolution of the quasi-thermal conductanceκl/r/T [see Eq. (8)] can be obtained numerically and the result after the ramping, i.e., for t >10ts = 200J0, is shown in Fig. 3(a). The curves in dif- ferent colors correspond to different reservoir lengths, ...

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[4] [4]

(12), the system can also be analyzed using the Landauer- Büttiker formula; see Refs

Comparison with the Landauer-Büttiker formalism Beyond the direct time-evolution calculations based on Eq. (12), the system can also be analyzed using the Landauer- Büttiker formula; see Refs. [51–53] for previous applications to Majorana-related transport problems. Using Eq. (11), we evaluate the thermal conductance from the Landauer-Büttiker formula and...

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[5] [5]

Influence of coupling strength To systematically explore different transport regimes, we analyze the transmission spectrumT (ω) by varying the cou- pling strength JT . The interplay between the broadening Γl/r∝J2 T and the discrete energy level structure of the finite- sized channel leads to qualitatively distinct behaviors, depend- ing on whether Γl/r is...

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[6] [6]

(9)], the thermal conductance is obtained by integrating T (ω) against the difference in occupation functions

Influence of temperature According to the Landauer-Büttiker formalism [Eq. (9)], the thermal conductance is obtained by integrating T (ω) against the difference in occupation functions. In particu- lar, by setting T (ω) = 1 in Eq. (9), one obtains the result κ/T = π/12 (in natural units with kB = ℏ = 1), which cor- responds to the half-quantized value [24...

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[7] [7]

Dependence on coupling strength, magnetic field, and temperature Building on the understanding established via the Landauer-Büttiker analysis, we now examine the thermal con- ductance calculated from the direct time-evolution calculation (see Sec. II C 1). As shown in Fig. 5(a) with h = 0.1J0, which is the same field used in Fig. 4(c), the conductance dep...

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[8] [8]

Specifically, we find that the half- quantized thermal conductance can emerge at higher temper- atures when the coupling strength is appropriately tuned

Enhancing quantized conductance at higher temperatures via finite-size effects While our earlier analysis emphasized the necessity of ul- tralow temperatures for observing half-quantized thermal con- ductance, primarily due to finite-size-induced suppression of transmission away from ω = 0, a notable exception emerges under special conditions. Specificall...

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