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Anyon Exchange Phase from Antidot Interferometry

T0 review · 0 major / 4 minor · reviewed 2026-07-14 · grok-4.5

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Pith's one-line read The anyon exchange phase itself can be read from transmission-phase plateaus across a single antidot resonance in a Fabry–Perot interferometer.

desk verdict Clean microscopic theory that turns the Kivelson-Murthy antidot idea into a readable plateau difference equal to the bare exchange phase heta=πν. read the letter →

arxiv 2606.24831 v2 pith:O6A3S7WG submitted 2026-06-23 cond-mat.mes-hall cond-mat.str-el

Matthias Thamm , Felix Puster , Bernd Rosenow This is my paper
classification cond-mat.mes-hallcond-mat.str-el PACS 73.43.Jn71.10.Pm05.30.Pr
keywords anyonsexchangephasefractionalquantumHallantidotFabry–PerotinterferometerKeldyshtransportLaughlinstatetransmission
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

Fractional quantum Hall quasiparticles are anyons: they carry a fraction of the electron charge and pick up a fractional phase when two of them are exchanged. Charge and the full braiding phase (twice the exchange phase) have already been measured, but the exchange phase itself has stayed out of reach. This paper shows that embedding a gate-tunable quantum antidot in one arm of a Fabry–Perot interferometer makes that phase accessible. When a plunger gate sweeps a single antidot level through resonance, the transmission phase of the interference current settles on two plateaus whose difference equals the bare exchange phase πν. The same calculation predicts a non-monotonic swing of the phase near the lead chemical potentials—unlike the familiar monotonic 0-to-π rise for ordinary electrons. The result is intended as a concrete blueprint for an ongoing experiment that aims to measure the exchange phase directly.

What carries the argument

Third-order Keldysh expansion of the Aharonov–Bohm current through the antidot, with anyonic statistics carried by Klein factors and with the antidot Green function dressed by a non-equilibrium occupation n(Vg) and a self-energy that supplies level broadening Γ(ε) and shift Λ(ε). The plateau difference of the resulting transmission phase δ(Vg) isolates θ.

What would settle it

In a gate-screened antidot interferometer, measure the transmission phase while sweeping a single level through resonance: if the plateau difference is not πν (for filling ν) and the phase does not show the predicted non-monotonic swing near ±ΔV/2, the claim fails.

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Extended reading notes

Core claim

For Laughlin anyons the difference between the transmission-phase plateaus on either side of a single, gate-screened antidot resonance equals the bare exchange phase θ = πν. A systematic non-equilibrium Keldysh calculation that includes the antidot’s occupation and anyonic level broadening produces a non-monotonic phase evolution near the lead chemical potentials, in clear contrast to the monotonic Breit–Wigner evolution of electrons.

Load-bearing premise

The antidot charge must be screened almost entirely by an external gate; if the quantum-Hall edges do the screening instead, an electrostatic phase exactly cancels the statistical phase one wants to measure.

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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 4 minor

Summary. The manuscript develops a non-equilibrium Keldysh theory for a Fabry–Perot interferometer containing a quantum antidot in one arm, tuned through resonance by a plunger gate. For Laughlin anyons the transmission phase of the Aharonov–Bohm current evolves non-monotonically across a single resonance (in contrast to the monotonic 0 oπ Breit–Wigner evolution for electrons). The difference between the asymptotic phase plateaus equals the bare exchange phase θ=πν, provided the antidot charge is screened by an external gate and the level spacing exceeds the bias window. The calculation incorporates Klein factors, power-law edge densities of states, non-equilibrium antidot occupation, and self-energy level broadening, and recovers the electron T-matrix and the Chamon–Wen sequential-tunneling current as consistency checks.

Significance. If the result holds, the work supplies a concrete, experimentally accessible protocol for measuring the anyonic exchange phase itself rather than only the braiding phase 2θ. The non-monotonic phase evolution is a sharp, falsifiable prediction for ongoing antidot-interferometer experiments. Strengths include an internally consistent derivation from chiral Luttinger liquids and Klein factors (no hand-inserted statistics), explicit validity windows (r≪1), recovery of known limits, and a clear statement of the gate-screening prerequisite that isolates the statistical phase from electrostatic contributions.

minor comments (4)
  1. Fig. 2 caption and main-text discussion of the dashed-line regions (r>0.5) could more explicitly remind the reader that the plateau values used for readout of θ lie outside those regions, so the extraction remains quantitative.
  2. End Matter, Klein-factor contour: a short sentence clarifying that observables are independent of the precise origin choice would help readers less familiar with the Altland–Gefen–Rosenow construction.
  3. Supplemental Material A: the Friedel-sum-rule cancellation argument is clear, but a one-sentence estimate of the gate-screening fraction f achievable with a graphite back-gate (or similar) would strengthen the experimental outlook without altering the formal claim.
  4. Notation: the same symbol Γ is used both for the gamma function and for level broadening; a brief local redefinition or subscript would remove the minor ambiguity noted in the End Matter.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the exchange phase enters via standard Klein factors and is recovered as a derived plateau difference by explicit Keldysh calculation.

full rationale

The paper is a self-contained theoretical proposal. Anyonic statistics are introduced in the usual way through Klein-factor commutation relations (End Matter, Eq. (4) and the contour choice of Ref. [44]), which produce the factor e^{iπν} in the third-order Keldysh current (Eq. (5)) and in the resummed transmission amplitude (Eq. (10)). The T-matrix benchmark for electrons (Eq. (3)) shows how the corresponding fermionic factor cancels against the intermediate-state sign, leaving only the Breit-Wigner phase; for Laughlin anyons the fractional factor survives and appears as the difference between the transmission-phase plateaus on either side of a single resonance. Non-equilibrium occupation (Eq. (9)) and level broadening are obtained from a self-energy that is consistent with the sequential-tunneling result of Chamon & Wen; they are not fitted to the target observable. The gate-screening condition (Supp. Mat. A) is stated as a necessary experimental prerequisite, not as a hidden assumption that forces the result. There is no self-definitional loop, no parameter fitted to data and then re-predicted, and no load-bearing uniqueness theorem imported from the authors’ prior work. The derivation therefore stands as an independent calculation of a measurable signature of the input statistics.

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

The calculation rests on standard chiral-Luttinger-liquid and anyon-statistics axioms plus one device-specific electrostatic assumption. No free parameters are fitted to data; all numerical curves are generated from the derived expressions.

assumptions (4)
  • domain assumption Fractional quantum Hall edges are chiral Luttinger liquids with tunneling density of states ∼ |ε|ν−1
    Used throughout the Green-function construction (Eqs. 5–10 and End Matter).
  • domain assumption Anyonic statistics are carried by Klein factors with exchange phases e^{iπν}
    Fixed by the contour choice (Eq. 4 and End Matter); the plateau difference is traced directly to these phases.
  • ad hoc to paper Antidot charge is screened by an external gate so that the electrostatic phase does not cancel θ
    Stated as necessary for observability (Supplemental Material A); without it the central claim fails.
  • domain assumption Single-level approximation valid when level spacing ≫ bias and temperature
    Invoked to reduce the antidot Green function to Eq. 6 and to isolate one resonance.

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Pith. "Pith review of Anyon Exchange Phase from Antidot Interferometry." pith.science (2026). https://pith.science/paper/O6A3S7WG

@misc{pith2026260624831,
  author       = {Pith},
  title        = {Pith review of: Anyon Exchange Phase from Antidot Interferometry},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O6A3S7WG}},
  note         = {Machine review of arXiv:2606.24831}
}
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.

Figures

Figures reproduced from arXiv: 2606.24831 by the authors.

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. 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￾gions in whic… view at source ↗
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 1/2; at Vg… view at source ↗
Figures from the paper (1 more)
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:fi…

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