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arxiv: 2606.24831 · v1 · pith:O6A3S7WGnew · submitted 2026-06-23 · ❄️ cond-mat.mes-hall · cond-mat.str-el

Anyon Exchange Phase from Antidot Interferometry

Matthias Thamm , Felix Puster , Bernd Rosenow This is my paper

Pith reviewed 2026-06-25 22:27 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.str-el
keywords anyonexchange phasefractional quantum HallantidotFabry-Perot interferometerKeldysh formalismtransmission phasebraiding statistics
0
0 comments X

The pith

The bare anyon exchange phase is obtained from the difference between transmission phase plateaus around an antidot resonance.

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

This paper develops a route to the exchange phase of anyons, a quantity that has remained out of reach even after fractional charge and braiding phase have been measured. A quantum antidot is placed inside a Fabry-Perot interferometer; a non-equilibrium Keldysh calculation that keeps track of the antidot occupation and its level broadening is performed while a gate voltage sweeps the antidot through resonance. The resulting transmission phase rises and then falls for anyons, producing two distinct plateaus whose difference equals the bare exchange phase; the same sweep for electrons yields only monotonic advance. The method therefore converts an interferometric observable into a direct readout of the anyon exchange phase.

Core claim

Within a systematic non-equilibrium Keldysh treatment that consistently includes the occupation and level broadening of the antidot, the transmission phase evolves non-monotonically when a gate voltage tunes the antidot through a resonance, in contrast to the monotonic evolution for electrons. The bare exchange phase can be extracted from the difference between the phase plateaus.

What carries the argument

The difference between the two transmission-phase plateaus that appear when the antidot is tuned through resonance under the Keldysh treatment that retains occupation and level broadening.

If this is right

  • The exchange phase of anyons becomes a measurable interferometric quantity rather than an inferred one.
  • Anyonic and fermionic statistics produce qualitatively different phase traces in the same device geometry.
  • The plateau-difference method supplies a new observable that can be combined with existing charge and braiding measurements.
  • The approach is formulated for fractional quantum Hall quasiparticles but relies only on the fractional exchange phase entering the scattering phase.

Where Pith is reading between the lines

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

  • The same antidot geometry might be used to compare exchange phases across different filling factors in a single cooldown.
  • If the plateau difference survives additional dephasing channels, the method could be adapted to interferometers that already demonstrate anyon braiding.
  • Numerical checks of the Keldysh equations for other fractional statistics would test whether the non-monotonic signature is universal for anyons.

Load-bearing premise

The non-equilibrium Keldysh treatment that includes occupation and level broadening produces a non-monotonic phase evolution for anyons whose plateau difference equals the bare exchange phase with no additional corrections.

What would settle it

An experimental trace showing strictly monotonic phase advance through the antidot resonance for anyons, or a measured plateau difference that deviates from the independently known exchange phase, would falsify the extraction procedure.

Figures

Figures reproduced from arXiv: 2606.24831 by Bernd Rosenow, Felix Puster, Matthias Thamm.

Figure 1
Figure 1. Figure 1: Fabry-Perot interferometer with a quantum an [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Transmission phase δ (upper panel) and oscilla￾tion amplitude I˜ (lower panel) for tunneling through a single antidot level, versus gate voltage Vg at several temperatures, for ν = 1/3 anyons and a = 0. The Aharonov-Bohm part of the current is Id,AB ∝ I˜cos(ϕAB + δ + π) [Eq. (10)], where the phase shift of π amounts to the Breit-Wigner phase below resonance, and ∆V is the bias between edges u and d. Re￾gio… view at source ↗
Figure 3
Figure 3. Figure 3: Non-equilibrium occupation n of the antidot [Eq. (9)] versus gate voltage Vg at several temperatures, for balanced couplings |γua| = |γad| = 0.25 e ∗∆V (QPC transmis￾sion of about 10–30%). The level fills as Vg increases, from empty at large negative Vg to full at large positive Vg. At Vg = −∆V /2 it aligns with the u-edge chemical potential and couples strongly to that edge, so the occupation rises above … view at source ↗
Figure 4
Figure 4. Figure 4: Transmission phase δ versus gate voltage Vg for tuning across two successive antidot levels, at kBT /e∗∆V = 0.025. The level spacing is ∆εa, so e ∗Vg/∆εa = 0 and 1 mark the two level crossings. Each crossing reproduces the non￾monotonic behavior of [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

Quasiparticles in fractional quantum Hall systems are anyons, carrying a fraction of the electron charge. Exchanging two of them gives rise to a fractional exchange phase. While the fractional charge and the braiding phase -- twice the exchange phase -- have been measured, the exchange phase itself has remained inaccessible. We study a quantum antidot embedded in a Fabry-Perot interferometer. Within a systematic non-equilibrium Keldysh treatment that consistently includes the occupation and level broadening of the antidot, we find that the transmission phase evolves non-monotonically when a gate voltage tunes the antidot through a resonance, in contrast to the monotonic evolution for electrons. The bare exchange phase can be extracted from the difference between the phase plateaus.

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 manuscript claims that a quantum antidot embedded in a Fabry-Perot interferometer, treated with a systematic non-equilibrium Keldysh formalism that includes occupation and level broadening, produces non-monotonic transmission-phase evolution when a gate voltage tunes the antidot through resonance for anyons, in contrast to the monotonic evolution found for electrons. From this contrast the authors conclude that the bare anyon exchange phase can be extracted directly from the difference between the resulting phase plateaus.

Significance. If the central extraction is rigorously shown to be free of residual Keldysh corrections, the result would supply the first direct access to the exchange phase itself, complementing existing measurements of fractional charge and braiding phase. The consistent non-equilibrium treatment is a methodological strength relative to equilibrium approximations commonly used in interferometry studies.

major comments (2)
  1. [Abstract] Abstract: the claim that 'the bare exchange phase can be extracted from the difference between the phase plateaus' is load-bearing for the entire result, yet the abstract supplies no derivation showing how anyonic statistics enter the Keldysh self-energies or transmission amplitude, nor an explicit demonstration that phase shifts arising from fractional statistics, charging, occupation, and level broadening cancel exactly in the plateau difference.
  2. [Keldysh calculation (results section)] The non-monotonic versus monotonic contrast is asserted to arise solely from the anyonic exchange phase. An explicit step-by-step derivation (or numerical check) is required to confirm that the Keldysh corrections from broadening and occupation do not contribute an additional phase offset that survives the subtraction; without this the extraction procedure remains unverified.
minor comments (1)
  1. [Abstract] The abstract would be clearer if it specified the filling factor or the model Hamiltonian used for the anyons.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and for identifying the need to make the extraction procedure fully explicit. The comments correctly highlight that the central claim requires a clear demonstration that non-statistical Keldysh contributions cancel in the plateau difference. We address each point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'the bare exchange phase can be extracted from the difference between the phase plateaus' is load-bearing for the entire result, yet the abstract supplies no derivation showing how anyonic statistics enter the Keldysh self-energies or transmission amplitude, nor an explicit demonstration that phase shifts arising from fractional statistics, charging, occupation, and level broadening cancel exactly in the plateau difference.

    Authors: The abstract is a concise summary; the explicit incorporation of anyonic statistics into the Keldysh self-energies (via the fractional phase factor in the tunneling amplitudes) and the resulting transmission phase is derived in the main text. We agree that a brief pointer in the abstract would strengthen clarity. In the revision we will add one sentence referencing the key equations that establish the cancellation in the plateau difference. revision: yes

  2. Referee: [Keldysh calculation (results section)] The non-monotonic versus monotonic contrast is asserted to arise solely from the anyonic exchange phase. An explicit step-by-step derivation (or numerical check) is required to confirm that the Keldysh corrections from broadening and occupation do not contribute an additional phase offset that survives the subtraction; without this the extraction procedure remains unverified.

    Authors: We acknowledge that an explicit verification of the cancellation is necessary. The anyonic exchange phase enters as an additional phase shift in the resonant tunneling amplitude that is absent for electrons; the occupation and broadening corrections appear symmetrically in both cases and therefore subtract when the plateau difference is taken. In the revised manuscript we will insert a dedicated paragraph (or short subsection) providing the analytical steps that isolate this cancellation, confirming that residual Keldysh offsets vanish in the difference. revision: yes

Circularity Check

0 steps flagged

No circularity: central result follows from explicit Keldysh calculation

full rationale

The paper performs a systematic non-equilibrium Keldysh treatment that incorporates occupation and level broadening, derives non-monotonic transmission-phase evolution specifically for anyons (contrasted with monotonic evolution for electrons), and states that the bare exchange phase follows from the difference of the resulting phase plateaus. This chain is self-contained: the non-monotonicity and the extraction step are outputs of the calculation rather than inputs redefined or fitted parameters renamed as predictions. No self-definitional loop, no fitted-input-called-prediction, and no load-bearing self-citation chain is present in the provided derivation outline. The result is therefore independent of its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The proposal rests on standard properties of anyons in the fractional quantum Hall effect and on the applicability of the Keldysh formalism to the interferometer; no new free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Anyons in fractional quantum Hall systems carry fractional charge and exhibit a fractional exchange phase upon particle exchange.
    Stated in the opening sentences as background for the measurement problem.
  • standard math The non-equilibrium Keldysh formalism consistently incorporates antidot occupation and level broadening to compute transmission phase.
    Invoked as the calculational framework that produces the non-monotonic behavior.

pith-pipeline@v0.9.1-grok · 5650 in / 1301 out tokens · 25580 ms · 2026-06-25T22:27:27.023088+00:00 · methodology

discussion (0)

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