REVIEW 3 major objections 3 minor 57 references
Observation of Time-Domain Braiding of Non-Abelian Anyons at $\nu = 5/2$ State
T0 review · 3 major / 3 minor · reviewed 2026-08-15 · deepseek-v4-flash
Pith's one-line read Shot-noise measurements at the ν=5/2 fractional quantum Hall state match, without fitting parameters, theoretical predictions for time-domain braiding of charged Abelian anyons and upstream non-Abelian neutral anyons in the particle-hole…
desk verdict A credible but conditional experimental claim of non-Abelian time-domain braiding at ν=5/2; the charge-channel PH-Pf vs A-Pf distinction is clean, but the untested 1.4 μm fixed-point assumption leaves room for alternative equilibration explanations. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the time-domain braiding loop. A quasiparticle excitation at the detection QPC, with energy of order $k_B T$, can tunnel out and tunnel back within a time window of order $\hbar/k_B T$; these two trajectories are indistinguishable and interfere, forming a closed loop in the (1+1)-dimensional spacetime of the edge. Any dilute anyon that passes the QPC within this window is enclosed by the loop and braided with the excited anyon's charged or neutral component. The unit monodromies are $M_c=e^{-i\pi/4}$ for the charged Abelian anyon and $M_n=0$ for the neutral non-Abelian Ising anyon; the relative weight of braiding versus trivial partition noise is controlled by the total scaling dimension $\delta=\delta_c+\delta_n$, which is $1/4$ for the PH-Pf edge and $1/2$ for the anti-Pfaffian edge. The experimental Fano factors are computed by substituting the measured reflection probabilities into the theoretical expressions, so the comparison involves no fitting parameters.
What would settle it
Measure the neutral Fano factor in a device whose two point contacts are separated by a distance much larger than the expected phase-coherence length (for example, 10 micrometres); if the excess neutral noise at the detection drain stays at the same magnitude, the signal cannot be time-domain braiding and would point instead to incoherent heating or equilibration of the edge modes.
Extended reading notes
Core claim
On its own terms, the paper's central claim is that the excess shot noise generated when a dilute beam of $e/4$ quasiparticles is partitioned by a second quantum point contact is dominated by 'time-domain braiding': a thermally excited quasiparticle tunnels across the detection QPC and tunnels back within the energy-time uncertainty window $\hbar/k_B T$, forming a closed loop in time, and any dilute anyons passing the QPC within that window are enclosed by the loop and acquire a braiding monodromy. For the charged-anyon configuration the relevant unit monodromy is $M_c=e^{-i\pi/4}$; for the neutral-anyon configuration the relevant unit monodromy is $M_n=0$, the hallmark of non-Abelian Ising anyons, for which braiding takes the state into an orthogonal state. The measured noise at the detection drains, normalized to Fano factors $\mathcal{F}_{\rm charge}$ and $\mathcal{F}_{\rm neutral}$, agrees with the theoretical predictions for the PH-Pf edge, whose charged and neutral scaling dimensions are $\delta_c=\delta_n=1/8$, and lies closer to PH-Pf than to anti-Pfaffian in the charged-anyon configuration. The agreement is obtained without fitting parameters.
Load-bearing premise
The whole interpretation rests on the assumption that the 1.4-micrometre edge segment between the two point contacts is phase-coherent and free of charge or thermal equilibration, so the neutral braiding effect is exactly zero; if that segment equilibrates, the extra neutral noise could come from incoherent heating rather than braiding.
Editorial extensions
If this is right
- If the central claim is right, shot-noise measurements of this kind constitute a direct, parameter-free probe of non-Abelian braiding statistics that does not require spatial interferometry.
- The data single out the particle-hole Pfaffian order over the anti-Pfaffian order, in line with earlier thermal Hall measurements.
- The same two-QPC scheme can be extended to other candidate non-Abelian states, such as the anti-Read-Rezayi state at $\nu=12/5$ or the $\nu=1/2$ state in wide quantum wells.
- The order-of-magnitude estimate in the paper rules out incoherent heating of the neutral mode as the origin of the excess neutral noise.
Reading between the lines
- If the braiding interpretation is correct, the neutral Fano factor near 2.3 should be insensitive to the transmission of the injection QPC; a strong dependence would instead point to subdominant processes dominating the signal.
- The same time-domain loop picture predicts that the charged Fano factor should approach the Poisson-limit value 1.5 in the high-dilution limit, a regime that could be checked in devices with much weaker injection-QPC reflection.
- A direct test would be the temperature dependence: as $T$ rises, the $\hbar/k_B T$ time window shrinks, so the braiding-induced excess noise should decrease with temperature in a way that an incoherent heating model would not reproduce.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript reports shot-noise measurements on the ν=5/2 fractional quantum Hall edge in two complementary two-QPC geometries. In the charged-anyon configuration, a dilute beam of e/4 quasiparticles generated at QPC2 impinges on QPC1, and the measured excess noise gives a charge Fano factor of 1.54 at e*V_S/(2k_BT)=4.6, compared with the PH-Pf prediction 1.49 and the A-Pf prediction 0.94. In the neutral-anyon configuration, upstream neutral anyons generated at QPC1 propagate to QPC2, and the measured neutral Fano factor is 2.37 at e*V_S/(2k_BT)=5.0, compared with the PH-Pf prediction 2.33 and the A-Pf prediction 2.0. The theoretical curves are obtained from CFT edge models and measured QPC reflection probabilities, with no experimental fitting parameters. The authors conclude that the two independent measurements together provide evidence for time-domain braiding of non-Abelian neutral anyons and that the edge realizes the particle-hole Pfaffian (PH-Pf) topological order.
Significance. If correct, this would be a milestone: the first time-domain braiding evidence for non-Abelian anyons and a clean PH-Pf versus A-Pf discriminator in the charge configuration. The paper's strengths include four data sets from three devices, independent probes of the downstream charged and upstream neutral anyon beams, and a detailed theoretical treatment in Supplementary Note 2 that includes time-domain braiding, trivial partitioning, intermediate processes, and subleading braiding channels. The comparison is parameter-free in the sense that the CFT parameters are fixed by the topological order, and the measured reflection probabilities enter as inputs. The neutral-anyon configuration, even if not by itself fully discriminating PH-Pf from A-Pf, is a novel direct probe of the upstream non-Abelian sector. These features make the work potentially very significant for the quantum Hall and topological quantum computation communities.
major comments (3)
- [Figures 2b, 3b, and S1–S4] No error bars or quantitative uncertainty estimates are shown in any of the noise or Fano-factor plots, yet the text repeatedly claims agreement 'within experimental uncertainty' (main text discussion of Figs. 2b and 3b; Supplementary Note 1). This is load-bearing because the PH-Pf and A-Pf predictions in the neutral configuration differ by only about 0.3 in the Fano factor (F=2.33 versus 2.0 at the representative point, with measured F=2.37), and the statement that the data are 'slightly closer' to PH-Pf cannot be evaluated without a quantitative uncertainty budget. The authors should provide error bars, confidence intervals, or at minimum a stated uncertainty budget for the extracted Fano factors.
- [Methods, 'Theory of the Fano factors'; main text, 'Time-domain braiding of neutral anyons'] The calculation assumes that the 1.4 μm inter-QPC separation is shorter than the inter-mode equilibration lengths, i.e., that the edge segment realizes the ideal PH-Pf fixed point. This assumption is explicitly stated but not independently established. The incoherent-heating model in Supplementary Note 3 treats only the opposite hierarchy l_ch-eq << L, and the intermediate regime l_ch-eq ~ L is not considered; partial inter-mode equilibration could produce excess neutral noise that is neither the braiding prediction nor the heating prediction. Since the neutral Fano factor is normalized by the separately measured differential reflection probability R_QPC2^diff, a partial-equilibration model could in principle mimic the observed values without invoking braiding. The authors should provide a diagnostic that validates the fixed-point and coherence assumption, such as a length-dependence measurement, a bias-dependence check, or an independent equilibration probe.
- [Supplementary Note 1 vs. main text, Fig. 3b discussion] Supplementary Note 1 states that in the neutral-anyon configuration the data 'also agree well with the PH-Pf prediction, although the A-Pf prediction lies closer to the measured values,' whereas the main text states that the data are 'slightly closer to the PH-Pf prediction.' This inconsistency is material because the two configurations are presented as cross-validating the PH-Pf order. If the representative data set of Fig. 3b is the exception rather than the rule, this should be stated explicitly, and the combined-evidence argument should be reformulated accordingly.
minor comments (3)
- [Methods, Eq. (7) and accompanying text; Supplementary Note 2D] The numerical factors C_rd^c and C_rd^n are introduced in the main text only as 'numerical factors.' Their values (0.47, 0.44, 0.09, and 0.59 in Supplementary Note 2D) and the fact that they are internal calibration constants obtained by comparing saddle-point and exact numerical integration should be stated in the main text, so that the 'without any fitting parameter' claim is unambiguous.
- [Supplementary Note 3] There is a typo in the definition of the thermal equilibration length: 'legnth' should read 'length.'
- [Main text, after Eq. (2)] The binomial distribution is said to be 'approximately described' for weaker dilutions, but no criterion is given for when the binomial approximation is valid. Since R_iQPC values are not tabulated for the four data sets, the authors should state the range of R_iQPC used and justify the binomial approximation in that range.
Circularity Check
No significant circularity: the Fano-factor predictions are parameter-free external tests using prior CFT inputs and measured QPC transmissions.
full rationale
The central comparison is a genuine external test. The theoretical Fano factors F_charge^th and F_neutral^th are computed from the CFT parameters (M_c, M_n, delta_c, delta_n) and the measured reflection probabilities, with no parameter fitted to the noise data. The PH-Pf and A-Pf predictions differ, and the data favor PH-Pf, especially in the charged-anyon configuration (measured F_charge = 1.54 vs 1.49 for PH-Pf and 0.94 for A-Pf). The self-citations [24-26] supply the theoretical method, but that method was published and tested before this experiment; the present data are an additional falsifiable test, not an input to the theory. The main caveat, that the 1.4 micrometer inter-QPC segment is assumed to be in the ideal PH-Pf fixed-point regime, is a stated premise in the Methods: 'The calculation assumes that the inter-QPC separation of 1.4 um is shorter than the inter-mode equilibration lengths.' The sentence in the main text that 'the agreement between the experimental data and the PH-Pf theory implies that this condition is met' is a consistency inference, not a constructional equivalence. An untested intermediate equilibration regime could in principle produce similar noise, but that is a scientific robustness concern, not a circularity. No step in the derivation reduces a prediction to its input by definition or by fit.
Assumptions & free parameters
free parameters (4)
- C_rd^c,PH-Pf =
0.47
- C_rd^n,PH-Pf =
0.44
- C_rd^c,A-Pf =
0.09
- C_rd^n,A-Pf =
0.59
assumptions (5)
- domain assumption The ν=5/2 fractional quantum Hall state is described by one of the Pfaffian, anti-Pfaffian, or particle-hole Pfaffian topological orders hosting Ising non-Abelian anyons.
- domain assumption The PH-Pf edge is described by a chiral CFT with a downstream charge boson and an upstream Majorana mode, and the e/4 quasiparticle operator is Ψ=e^{iφ/2}σ with scaling dimensions δ_c=1/8 and δ_n=1/8.
- domain assumption The inter-QPC separation L=1.4 μm is shorter than phase-coherence and equilibration lengths, so the injected dilute beam remains coherent between the two QPCs.
- ad hoc to paper The injected dilute anyon beam obeys binomial statistics with n=I_S(t2-t1)/e*, used to compute the average monodromy.
- domain assumption Lowest-order perturbation theory in the detection QPC tunneling, including time-domain braiding, trivial partitioning, and intermediate processes, captures the measured noise.
Cite this review
Pith. "Pith review of Observation of Time-Domain Braiding of Non-Abelian Anyons at $\nu = 5/2$ State." pith.science (2026). https://pith.science/paper/JULRZ3CQ
@misc{pith2026260812897,
author = {Pith},
title = {Pith review of: Observation of Time-Domain Braiding of Non-Abelian Anyons at $\nu = 5/2$ State},
year = {2026},
howpublished = {\url{https://pith.science/paper/JULRZ3CQ}},
note = {Machine review of arXiv:2608.12897}
}
abstract
Unlike elementary particles, which obey either bosonic or fermionic exchange statistics, certain quasiparticles, known as anyons, are predicted to exhibit Abelian or non-Abelian braiding statistics. While braiding Abelian anyons modifies the wavefunction by a 'statistical phase', braiding non-Abelian anyons implements a unitary transformation of the state within a degenerate subspace of states. Experimental evidence of non-Abelian braiding has thus far remained elusive. Here, we report a 'time-domain braiding' signature of non-Abelian anyons in the $\nu = 5/2$ fractional quantum Hall state, by extending our previously demonstrated approach with Abelian anyons at $\nu = 1/3$. Our approach is based on measurements of the current fluctuations arising from weak partitioning of a highly dilute one-dimensional edge mode. We independently probe the partition noise of the downstream charged mode and also that of the upstream neutral mode. These independent measurements agree with our theoretical predictions for 'time-domain braiding' of the downstream Abelian and the upstream non-Abelian anyons, respectively, in the 'particle-hole Pfaffian' topological order. Together, these results provide evidence for the presence of non-Abelian anyons.
Reference graph
Works this paper leans on
-
[1]
J. M. Leinaas and J. Myrheim, On the theory of identical particles. Il Nuovo Cimento B Series 37, 1 (1977)
work page 1977
-
[2]
B. I. Halperin, Statistics of quasiparticles and the hierarchy of fractional quantized Hall states, Phys. Rev. Lett. 52, 1583 (1984)
work page 1984
- [3]
-
[4]
G. Moore and N. Read, Non-Abelian in the fractional quantum Hall effect, Nucl. Phys. B360, 362 (1991)
work page 1991
-
[5]
M. Greiter, X.-G. Wen, and F. Wilczek, Paired Hall State at Half Filling, Phys. Rev. Lett. 66, 3205 (1991)
work page 1991
-
[6]
C. Nayak and F. Wilczek, 2𝑛𝑛-quasihole states realize 2𝑛𝑛−1-dimensional spinor braiding statistics in paired quantum Hall states, Nucl. Phys. B 479, 529 (1996)
work page 1996
-
[7]
E. Fradkin, C. Nayak, A. Tsvelik, and F. Wilczek, A Chern-Simons effective field theory for the Pfaffian quantum Hall state, Nucl. Phys. B 516, 704 (1998)
work page 1998
-
[8]
N. Read and D. Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect, Phys. Rev. B 61, 10267 (2000). 14
work page 2000
Show all 57 references
-
[9]
Nayak, S
C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non -Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083 (2008)
2008
-
[10]
Willett et al., Observation of an Even- Denominator Quantum Number in the Fractional Quantum Hall Effect, Phys
R. Willett et al., Observation of an Even- Denominator Quantum Number in the Fractional Quantum Hall Effect, Phys. Rev. Lett. 59, 1776 (1987)
1987
-
[11]
Stern and B
A. Stern and B. I. Halperin, Proposed experiments to probe the non-Abelian ν=5/2 quantum Hall state, Phys. Rev. Lett. 96, 016802 (2006)
2006
-
[12]
Bonderson, A
P. Bonderson, A. Kitaev, and K. Shtengel, Detecting non -Abelian statistics in the ν=5/2 fractional quantum Hall state, Phys. Rev. Lett. 96, 016803 (2006)
2006
-
[13]
D. E. Feldman and A. Kitaev, Detecting non -Abelian statistics with an electronic Mach- Zehnder interferometer, Phys. Rev. Lett. 97, 186803 (2006)
2006
-
[14]
S.-S. Lee, S. Ryu, C. Nayak, and M. P. A. Fisher, Particlehole symmetry and the ν=5/2 quantum Hall state, Phys. Rev. Lett. 99, 236807 (2007)
2007
-
[15]
Levin, B
M. Levin, B. Halperin, and B. Rosenow, Particle-hole symmetry and the Pfaffian state, Phys. Rev. Lett. 99, 236806 (2007)
2007
-
[16]
Dolev et al., Observation of a quarter of an electron charge at the ν=5/2 quantum Hall state, Nature 452, 829 (2008)
M. Dolev et al., Observation of a quarter of an electron charge at the ν=5/2 quantum Hall state, Nature 452, 829 (2008)
2008
-
[17]
I. P. Radu et al., Quasi-particle properties from tunneling in the ν=5/2 fractional quantum Hall state, Science 320, 899 (2008)
2008
-
[18]
R. L. Willett, L. N. Pfeiffer, and K.W. West, Measurement of filling factor 5/2 quasiparticle interference with observation of charge e/4 and e/2-period oscillations, Proc. Natl. Acad. Sci. U.S.A. 106, 8853 (2009)
2009
-
[19]
A. Bid, N. Ofek, H. Inoue, M. Heiblum, C. L. Kane, V. Umansky, and D. Mahalu, Observation of neutral modes in the fractional quantum Hall regime, Nature 466, 585 (2010)
2010
-
[20]
Banerjee, M
M. Banerjee, M. Heiblum, V. Umansky et al., Observation of half -integer thermal Hall conductance, Nature 559, 205 (2018)
2018
-
[21]
Dutta et al., Distinguishing between non- abelian topological orders in a quantum Hall system, Science 375, 193 (2021)
B. Dutta et al., Distinguishing between non- abelian topological orders in a quantum Hall system, Science 375, 193 (2021)
2021
-
[22]
R. L. Willett et al., Interference Measurements of Non -Abelian 𝑒𝑒/4 & Abelian 𝑒𝑒 /2 Quasiparticle Braiding, Phys. Rev. X 13, 011028 (2023)
2023
-
[23]
Kim et al., Aharonov–Bohm interference in even-denominator fractional quantum Hall states, Nature 649, 323 (2026)
J. Kim et al., Aharonov–Bohm interference in even-denominator fractional quantum Hall states, Nature 649, 323 (2026)
2026
-
[24]
M Lee et al., Partitioning of diluted anyons reveals their braiding statistics, Nature 617, 277 (2023)
J.-Y. M Lee et al., Partitioning of diluted anyons reveals their braiding statistics, Nature 617, 277 (2023)
2023
-
[25]
B. Lee, C. Han, H.-S. Sim, Negative Excess Shot Noise by Anyon Braiding. Phys. Rev. Lett. 123, 016803 (2019)
2019
-
[26]
J.-Y. M. Lee and H.-S. Sim, Non-Abelian Anyon Collider, Nat. Commun. 13, 6660 (2022)
2022
-
[27]
D. T. Son, Is the composite fermion a Dirac particle?, Phys. Rev. X 5, 031027 (2015)
2015
-
[28]
P. T. Zucker and D. E. Feldman, Stabilization of the particlehole Pfaffian order by Landau- level mixing and impurities that break particle-hole symmetry, Phys. Rev. Lett. 117, 096802 (2016)
2016
-
[29]
Lotric et al., Majorana edge reconstruction and the ν = 5/2 non -Abelian thermal Hall puzzle, arXiv: 2507.07161 (2025)
T. Lotric et al., Majorana edge reconstruction and the ν = 5/2 non -Abelian thermal Hall puzzle, arXiv: 2507.07161 (2025)
2025 arXiv
-
[30]
Nakamura et al., Direct observation of anyonc braiding statistics, Nat
J. Nakamura et al., Direct observation of anyonc braiding statistics, Nat. Phys. 16, 931 (2020)
2020
-
[31]
Kim et al., Aharonov– Bohm interference and statistical phase -jump evolution in fractional quantum Hall states in bilayer graphene, Nat
J. Kim et al., Aharonov– Bohm interference and statistical phase -jump evolution in fractional quantum Hall states in bilayer graphene, Nat. Nanotech. 19, 1619 (2024)
2024
-
[32]
Werkmeister et al., Anyon braiding and telegraph noise in a graphene interferometer, Science 388, 730 (2025)
T. Werkmeister et al., Anyon braiding and telegraph noise in a graphene interferometer, Science 388, 730 (2025). 15
2025
-
[33]
N. L. Samuelson et al., Slow Quasiparticle Dynamics and Anyonic Statistics in a Fractional Quantum Hall Fabry -Pérot Interferometer, Phys. Rev. X 16, 011062 (2026)
2026
-
[34]
Ghosh et al., Anyonic braiding in a chiral Mach-Zehnder interferometer, Nat
B. Ghosh et al., Anyonic braiding in a chiral Mach-Zehnder interferometer, Nat. Phys. 21, 1392 (2025)
2025
-
[35]
de-Picciotto et al., Direct observation of a fractional charge, Nature 389, 162 (1997)
R. de-Picciotto et al., Direct observation of a fractional charge, Nature 389, 162 (1997)
1997
-
[36]
Saminadayar et al., Observation of the e/3 fractionally charged Laughlin Quasiparticle, Phys
L. Saminadayar et al., Observation of the e/3 fractionally charged Laughlin Quasiparticle, Phys. Rev. Lett. 79, 2526 (1997)
1997
-
[37]
Rosenow, I
B. Rosenow, I. P. Levkivskyi, and B. I. Halperin, Current Correlations from a Mesoscopic Anyon Collider, Phys. Rev. Lett. 116, 156802 (2016)
2016
-
[38]
Bartolomei et al., Fractional statistics in anyon collisions, Science 368, 6487 (2020)
H. Bartolomei et al., Fractional statistics in anyon collisions, Science 368, 6487 (2020)
2020
-
[39]
Glidic et al., Cross -Correlation Investigation of Anyon Statistics in the ν = 1/3 and 2/5 Fractional Quantum Hall States, Phys
P. Glidic et al., Cross -Correlation Investigation of Anyon Statistics in the ν = 1/3 and 2/5 Fractional Quantum Hall States, Phys. Rev. X 13, 011030 (2023)
2023
-
[40]
Ruelle et al., Comparing Fractional Quantum Hall Laughlin and Jain Topological Orders with the Anyon Collider, Phys
M. Ruelle et al., Comparing Fractional Quantum Hall Laughlin and Jain Topological Orders with the Anyon Collider, Phys. Rev X 13, 011031 (2023)
2023
-
[41]
Han, J.-Y
C. Han, J.-Y. M. Lee, and H.-S. Sim, Anyon Interferometry to Detect Braiding Statistics of Neutral Modes, Phys. Rev. Lett. 133, 186603 (2024)
2024
-
[42]
R. A. Melcer, B. Dutta, C. Spånslätt, J. Park, A. D. Mirlin, V. Umansky, Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale, Nat Commun 13, 376 (2022)
2022
-
[43]
R. A. Melcer et al., Heat conductance of the quantum Hall bulk, Nature 625, 489 (2024)
2024
-
[44]
H. J. Kimble, M. Dagenais, and L. Mandel, Photon Antibunching in Resonance Fluorescence, Phys. Rev. Lett. 39, 691 (1977)
1977
-
[45]
Henny et al., The Fermionic Hanbury Brown and Twiss Experiment, Science 284, 296 (1999)
M. Henny et al., The Fermionic Hanbury Brown and Twiss Experiment, Science 284, 296 (1999)
1999
-
[46]
W. D. Oliver et al., Hanbury Brown and Twiss-Type Experiment with Electrons, Science 284, 299 (1999)
1999
-
[47]
Read and E
N. Read and E. Rezayi, Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level, Phys. Rev. B 59, 8084 (1999)
1999
-
[48]
S. K. Singh et al., Topological phase transition between Jain states and daughter states of the ν=1/2 fractional quantum Hall state, Nat. Phys. 20, 1247 (2024)
2024
-
[49]
Observation of Time-Domain Braiding of Non-Abelian Anyons atν= 5/2State
S Das Sarma, M. Freedman, and C. Nayak, Topologically protected qubits from a possible non -Abelian fractional quantum Hall state, Phys. Rev. Lett. 94, 166802 (2005). Supplementary Notes for “Observation of Time-Domain Braiding of Non-Abelian Anyons atν= 5/2State” Tomer Alkala...
2005
-
[50]
[S4, S5], we obtained the contributionC TDB 2m (t1−t 2) of the time-domain braiding to theC 2m term in Eq
Contribution from time-domain braiding Following the procedures of Refs. [S4, S5], we obtained the contributionC TDB 2m (t1−t 2) of the time-domain braiding to theC 2m term in Eq. (S10) at finite temperature. In Eqs. (S11) and (S13), time-domain braiding arises from time confi...
-
[51]
Contribution from trivial partitioning The trivial partitioning is illustrated in Fig. S7. In this partitioning, tunneling occurs at the detection QPC when an anyon from the diluted beam arrives there. The relevant energy scale of this process ise ∗VS, since the tunneling even...
-
[52]
Figure S8 illustrates the case of the charged-anyon configuration
Contribution from intermediate process There happens another subdominant process, which we call intermediate process, as its nature is intermediate between the trivial partitioning and the time-domain braiding. Figure S8 illustrates the case of the charged-anyon configuration....
-
[53]
This should be contrasted with the dominant time-domain braiding involving the vacuum channelIand the monodromyM n =M I→I (see Supplementary Note 2 D 1)
Contribution from other subleading braiding processes In the neutral-anyon configuration, subdominant time-domain braiding processes involving the fusion channelψ and the unit braiding monodromyM I→ψ can also occur. This should be contrasted with the dominant time-domain braid...
-
[54]
The factorI c/n denotes the exponents for the charged/neutral-anyon configuration
Time domain braiding Using the results in Supplementary Note 2 D 1, we obtained the tunneling rates from the time-domain braiding on the PH-Pf edge, W c/n,TDB m→d = W PH-Pf 0 2π2 sin(2πδ) Re h eiπδB δ+ Ic/n 2πkBT,δ− Ic/n 2πkBT sin πδ− Ic/n 2kBT i W c/n,TDB d→m = W PH-Pf 0 2π2 ...
-
[55]
Trivial Partitioning Using the results in Supplementary Note 2 D 2, we computed the tunneling rates arising from the trivial partitioning. For the charged-anyon configuration on the PH-Pf edge, the rates read W c,triv m→d =W PH-Pf 0 4π2 Cc,PH-Pf rd RiQPCfc triv δc,δn,e∗VS kBT ...
-
[56]
(S50) where the exponential factorIc follows Eqs
Intermediate Process Using the results in Supplementary Note 2 D 3, we computed the tunneling rates from the intermediate processes for the charged-anyon configuration on PH-Pf edge, W c,interm m→d =W PH-Pf 0 4π2 RiQPCfc interm δc,δn,e∗VS kBT × π Γ[2δ] − 1 cos(πδ) Re h Γ[δ+ Ic...
-
[57]
Subleading braiding process We finally comment on the subleading braiding process discussed in Supplementary Note 2 D 4. For the neutral- anyon configuration on the PH-Pf edge, the subleading-braiding contribution to the nonequilibrium Green function vanishes identically, as d...
2019
Reviewed August 15, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.