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arxiv: 2604.15133 · v1 · submitted 2026-04-16 · ❄️ cond-mat.mes-hall

Hanbury Brown-Twiss interferometry at the ν=2/5 fractional quantum Hall edge

Ryotaro Sano , Fumihiro Murabayashi , Daigo Ichikawa , Thibaut Jonckheere , J\'er\^ome Rech , Thierry Martin , Masayuki Hashisaka , Takeo Kato This is my paper

Pith reviewed 2026-05-10 09:51 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords Hanbury Brown-Twiss interferometryfractional quantum Hall effectν=2/5anyonic statisticsnoise correlationsedge statesweak tunneling
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0 comments X

The pith

A Hanbury Brown-Twiss setup at the 2/5 fractional quantum Hall edge produces flux-dependent noise with effective charge e/3.

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

The paper proposes a Hanbury Brown-Twiss interferometer in which quasiparticles tunnel between two co-propagating edge modes of a ν=2/5 fractional quantum Hall state. The setup is designed to rely on two-particle interference alone. Using a bosonized edge theory and Keldysh perturbation theory in the weak-tunneling regime, the authors derive the cross-correlation of the tunneling currents. In the limit of large device size this cross-correlation yields an analytic expression whose flux dependence mirrors that of an ordinary electronic HBT interferometer, except that the charge is replaced by the fractional value e^*=e/3 and the power-law exponents are set by the scaling dimensions of the fractional edge modes.

Core claim

In the large-device limit the flux-dependent cross-correlation noise takes an analytic form whose structure is identical to that of an ordinary electronic Hanbury Brown-Twiss interferometer, except that the electron charge is replaced by the fractional charge e^*=e/3 and the exponents are set by the scaling dimensions of the fractional edge modes.

What carries the argument

Bosonized theory of the two co-propagating ν=2/5 edge modes combined with Keldysh perturbation theory for the weak-tunneling current cross-correlations.

If this is right

  • The noise oscillates with magnetic flux at a period fixed by the fractional charge e/3.
  • The amplitude of the noise follows power laws determined by the scaling dimensions of the fractional quasiparticles rather than fermionic ones.
  • Any explicit dependence on the anyonic statistical angle drops out once the device size greatly exceeds the thermal length.
  • Reducing the device size toward the thermal length can reintroduce dependence on the anyonic angle in the cross-correlation.

Where Pith is reading between the lines

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

  • The construction isolates two-particle interference effects in a geometry that avoids single-particle phase accumulation.
  • Analogous noise measurements could be applied to other fractional filling factors to extract their scaling dimensions.
  • The large-device cancellation of anyonic phases suggests a practical route to fractional-charge detection that is less sensitive to geometric details than Mach-Zehnder or Fabry-Pérot interferometers.

Load-bearing premise

The device is large enough compared with the thermal length that anyonic exchange phases cancel from the observable noise.

What would settle it

A direct measurement of the cross-correlation noise in a sufficiently large ν=2/5 device that either confirms or rules out the predicted flux periodicity set by charge e/3.

Figures

Figures reproduced from arXiv: 2604.15133 by Daigo Ichikawa, Fumihiro Murabayashi, J\'er\^ome Rech, Masayuki Hashisaka, Ryotaro Sano, Takeo Kato, Thibaut Jonckheere, Thierry Martin.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of a Hanbury Brown–Twiss (HBT) inter [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Schematic of two interfering two-particle paths con [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Flux-dependent cross-correlation as a function of the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Temperature dependence of the flux-dependent cross [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Visibility of the flux-dependent cross-correlation, defined as [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

We propose a Hanbury Brown-Twiss interferometer for a $\nu=2/5$ fractional quantum Hall edge system, in which quasiparticles tunnel between two co-propagating edge modes. In contrast to the previously studied anyonic Fabry-P\'{e}rot and Mach-Zehnder interferometers, the proposed setup relies purely on two-particle interference rather than single-particle interference. In the weak-tunneling regime, we employ a bosonized edge theory together with Keldysh perturbation theory to evaluate the cross-correlation of the tunneling currents. In the large-device limit, we obtain an analytic expression for the flux-dependent noise, whose structure closely resembles that of an electronic HBT interferometer, but with the electron charge replaced by the fractional charge $e^{\star}=e/3$ and with scaling dimensions characteristic of the fractional edge modes. In this limit, the explicit anyonic exchange phases cancel, whereas when the device size becomes comparable to the thermal length, the cross-correlation may recover a more explicit dependence on the anyonic statistical angle.

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

2 major / 1 minor

Summary. The paper proposes a Hanbury Brown-Twiss (HBT) interferometer at the ν=2/5 fractional quantum Hall edge, with quasiparticles tunneling between two co-propagating modes. Using bosonized edge theory and Keldysh perturbation theory in the weak-tunneling regime, the authors derive an analytic expression for the flux-dependent cross-correlation noise in the large-device limit. This expression is claimed to resemble the electronic HBT form but with fractional charge e*=e/3 and the scaling dimensions of the fractional edge modes; anyonic exchange phases are stated to cancel explicitly in this limit, while recovering dependence on the statistical angle when device size is comparable to the thermal length.

Significance. If the central derivation holds, the result would provide a concrete, parameter-free prediction for two-particle interference noise at a hierarchical FQH edge, offering a potential experimental route to probe anyonic statistics via cross-correlations without relying on single-particle interference. The approach builds on standard tools (bosonization and Keldysh) and identifies a clean large-L regime where the noise reduces to a fractional-charge analog of the integer HBT interferometer.

major comments (2)
  1. [Abstract / Keldysh perturbation theory] Abstract and the Keldysh calculation: the claim that anyonic exchange phases cancel exactly in the large-device limit (device size ≫ thermal length) for the ν=2/5 hierarchical edge must be shown explicitly. The two co-propagating modes have distinct velocities and scaling dimensions; the multi-component boson commutators could leave residual phase factors in the contributing diagrams that would alter the flux dependence of the cross-noise, contrary to the stated resemblance to the electronic HBT form with only e*=e/3.
  2. [Derivation of cross-correlation noise] The analytic noise expression: the derivation should include explicit verification against limiting cases (e.g., equal velocities, vanishing anyonic angle, or device size approaching thermal length) to confirm that the flux-dependent term reduces precisely to the claimed form without additional phase or scaling corrections.
minor comments (1)
  1. [Abstract] The abstract refers to 'scaling dimensions characteristic of the fractional edge modes' without quoting the numerical values (e.g., for the charge and neutral modes at ν=2/5); these should be stated explicitly when the noise expression is introduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and will revise the manuscript accordingly to strengthen the presentation of the Keldysh calculation and its limits.

read point-by-point responses

  1. Referee: [Abstract / Keldysh perturbation theory] Abstract and the Keldysh calculation: the claim that anyonic exchange phases cancel exactly in the large-device limit (device size ≫ thermal length) for the ν=2/5 hierarchical edge must be shown explicitly. The two co-propagating modes have distinct velocities and scaling dimensions; the multi-component boson commutators could leave residual phase factors in the contributing diagrams that would alter the flux dependence of the cross-noise, contrary to the stated resemblance to the electronic HBT form with only e*=e/3.

    Authors: We agree that an explicit demonstration of the phase cancellation is required for clarity. In the revised manuscript we will expand the Keldysh section with a step-by-step evaluation of the contributing diagrams, showing how the commutators of the two-component bosonic fields for the ν=2/5 edge produce exact cancellation of the anyonic exchange phases in the large-L limit. The resulting flux dependence will be shown to involve only the fractional charge e*=e/3 together with the appropriate scaling dimensions, with no residual statistical phases. revision: yes

  2. Referee: [Derivation of cross-correlation noise] The analytic noise expression: the derivation should include explicit verification against limiting cases (e.g., equal velocities, vanishing anyonic angle, or device size approaching thermal length) to confirm that the flux-dependent term reduces precisely to the claimed form without additional phase or scaling corrections.

    Authors: We will add these verifications to the revised manuscript. We will explicitly recover the expected HBT-like form in the limits of equal velocities, vanishing anyonic angle, and device size comparable to the thermal length, confirming that the flux-dependent cross-noise reduces precisely to the stated expression without extraneous phase or scaling corrections. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses standard bosonization and Keldysh perturbation theory

full rationale

The central result—an analytic flux-dependent cross-noise in the large-device limit that reduces to an HBT-like form with e*=e/3 and fractional scaling dimensions—is obtained by applying established multi-component bosonization to the ν=2/5 edge and performing Keldysh perturbation theory in the weak-tunneling regime. The anyonic phase cancellation is stated as an explicit outcome of the large-L limit rather than an input assumption or fitted parameter. No self-citations are invoked as load-bearing uniqueness theorems, no ansatz is smuggled via prior work, and no fitted quantity is relabeled as a prediction. The derivation remains self-contained against external benchmarks of chiral Luttinger liquid theory and Keldysh formalism.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on established theoretical frameworks for modeling fractional quantum Hall edges without introducing new free parameters or postulated entities.

axioms (2)
  • domain assumption Bosonized edge theory accurately describes the co-propagating modes at ν=2/5
    Invoked to model quasiparticle tunneling between edge channels.
  • domain assumption Keldysh perturbation theory applies in the weak-tunneling regime
    Used to compute the cross-correlation of tunneling currents.

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