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arxiv: 2607.02188 · v1 · pith:QGM7ABMUnew · submitted 2026-07-02 · ❄️ cond-mat.mes-hall

Entropy of Non-Abelian Anyons from Slow Quasiparticle Dynamics in Quantum Hall Interferometers

Eran Sela , Mitali Banerjee This is my paper

Pith reviewed 2026-07-03 06:48 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords non-Abelian anyonsquantum Hall interferometeranyon entropyantidot chargefractional quantum Hallphase switchingMaxwell relations
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The pith

An antidot inside a quantum Hall interferometer can yield the O(1) entropy of non-Abelian anyons from equilibrium charge inferred via phase switching.

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

The paper proposes inferring the charge on a fractional antidot from the time-dependent switching of the interference phase observed in recent experiments. This non-local readout replaces conventional charge detectors and enables use of Maxwell relations to extract the entropy ΔS = k_B log d carried by non-Abelian anyons. The scheme operates at intermediate temperatures that sit above the interferometer edge level spacing yet well below the antidot level spacing, where the anyonic entropy contribution remains visible. For the u = 5/2 state this would directly give the factor √2 that distinguishes non-Abelian from Abelian quasiparticles.

Core claim

By embedding an antidot in an interferometer and using the recently observed time-dependent switching of the interference phase to infer the antidot charge at equilibrium, the characteristic O(1) entropy ΔS = k_B log d of non-Abelian anyons can be extracted via Maxwell relations for intermediate temperatures that exceed the level spacing of the interferometer edge but remain much smaller than the level spacing of the antidot.

What carries the argument

Inference of antidot charge from time-dependent switching of the interference phase, which serves as a non-local charge sensor at equilibrium.

If this is right

  • The entropy signal for d = √2 becomes accessible at filling factor 5/2 without direct charge sensing.
  • The method works only in the temperature window between edge and antidot level spacings.
  • It converts an existing experimental signature (phase switching) into a thermodynamic probe of anyonic statistics.

Where Pith is reading between the lines

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

  • Similar phase-switching readouts could be tested in other fractional states to map quantum dimensions across the hierarchy.
  • If the entropy extraction succeeds, it would supply an independent check on whether observed quasiparticles are indeed non-Abelian before braiding experiments are attempted.
  • The approach might be adapted to interferometers with multiple antidots to probe fusion channels or higher-order anyonic correlations.

Load-bearing premise

The observed time-dependent switching of the interference phase directly reports the antidot charge at equilibrium without calibration offsets or other systematics that would mask the entropy signal.

What would settle it

An experiment in which the entropy extracted from the inferred charge fluctuations fails to equal k_B log d (for example, showing zero instead of log √2 at u = 5/2) while the phase switching still occurs.

Figures

Figures reproduced from arXiv: 2607.02188 by Eran Sela, Mitali Banerjee.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of a device for measurement of non-Abelian [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Charge and entropy detection scheme via an antidot residing inside an interferometer. (a) The device contains a gate [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Non-Abelian anyons emerging in fractional quantum Hall states carry a characteristic entropy, $\Delta S = k_B \log d$, where \(d\) is the anyon's quantum dimension. This \(\mathcal{O}(1)\) entropy can, in principle, be extracted from charge measurements of an antidot via Maxwell relations. However, equilibrium charge measurements in fractional antidots have proven to be challenging with conventional charge detectors. Here, we propose a scheme based on an antidot embedded in an interferometer, in which the charge can be inferred from the recently observed time-dependent switching of the interference phase. Performing such non-local charge measurements at equilibrium, the characteristic \(\mathcal{O}(1)\) entropy of non-Abelian anyons (e.g., $d = \sqrt{2}$ for the $\nu = 5/2$ state) can be extracted for intermediate temperatures, which exceed the level spacing of the interferometer edge, but are much smaller than the level spacing of the antidot.

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

3 major / 2 minor

Summary. The manuscript proposes extracting the characteristic entropy ΔS = k_B log d of non-Abelian anyons (e.g., d=√2 at ν=5/2) from equilibrium antidot charge Q(T,μ) via Maxwell relations. The charge is to be inferred non-locally from the recently observed time-dependent switching of the interference phase in an antidot-embedded quantum Hall interferometer, in the temperature window set by edge level spacing ≪ T ≪ antidot level spacing.

Significance. If the inference of Q from phase switching can be shown to achieve the required ~0.1e precision without unquantified systematics, the approach would provide a concrete experimental route to the O(1) anyonic entropy that has so far eluded direct measurement. The proposal builds on existing interferometer observations and avoids conventional charge detectors, which is a genuine strength; however, the manuscript supplies no derivations, error budgets, or numerical checks, so the practical significance cannot yet be assessed.

major comments (3)
  1. [Abstract / proposal description] The central claim that phase-switching events yield equilibrium antidot charge Q at the precision needed to resolve ΔS ~ k_B log √2 rests on two unverified conditions: (i) the system remains in true thermal equilibrium on the antidot during switching, and (ii) edge-state or dynamical contributions to the phase can be subtracted to better than the target entropy scale. Neither condition is demonstrated analytically or numerically; the temperature window is stated but not shown to suppress corrections below ~0.1e.
  2. [Abstract] No Maxwell-relation derivation, thermodynamic identity, or finite-temperature correction is supplied to convert the inferred Q(T,μ) into ΔS; the abstract asserts that the entropy “can be extracted” but provides neither the explicit relation nor an estimate of the required charge resolution.
  3. [Proposal section (inferred from abstract)] The manuscript contains no error analysis, Monte-Carlo simulation of phase-to-charge conversion, or estimate of systematic offsets from non-equilibrium quasiparticle dynamics; without these, it is impossible to judge whether the O(1) entropy signal survives the measurement protocol.
minor comments (2)
  1. [Abstract] Notation for the anyonic dimension d and the temperature window should be introduced with explicit inequalities rather than prose only.
  2. [N/A] The manuscript would benefit from a schematic figure showing the interferometer geometry, antidot, and the phase-switching observable.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and for identifying key areas where the proposal requires additional analytical support. We agree that the manuscript, as a concise proposal, would benefit from explicit derivations and estimates to allow assessment of the scheme's viability. We will revise the manuscript to incorporate these elements while preserving its focus on the non-local measurement approach. Point-by-point responses follow.

read point-by-point responses

  1. Referee: [Abstract / proposal description] The central claim that phase-switching events yield equilibrium antidot charge Q at the precision needed to resolve ΔS ~ k_B log √2 rests on two unverified conditions: (i) the system remains in true thermal equilibrium on the antidot during switching, and (ii) edge-state or dynamical contributions to the phase can be subtracted to better than the target entropy scale. Neither condition is demonstrated analytically or numerically; the temperature window is stated but not shown to suppress corrections below ~0.1e.

    Authors: We acknowledge that the conditions for equilibrium and the suppression of corrections were stated but not derived in detail. In the revised manuscript we will add an analytical section demonstrating that, within the window edge level spacing ≪ T ≪ antidot level spacing, the antidot remains in thermal equilibrium on the timescale of the observed switching events. We will also derive bounds on edge-state phase contributions and show how they can be subtracted using the time-dependent data, with corrections falling below the ~0.1e threshold needed for ΔS resolution. revision: yes

  2. Referee: [Abstract] No Maxwell-relation derivation, thermodynamic identity, or finite-temperature correction is supplied to convert the inferred Q(T,μ) into ΔS; the abstract asserts that the entropy “can be extracted” but provides neither the explicit relation nor an estimate of the required charge resolution.

    Authors: The abstract refers to extraction via Maxwell relations, but we agree an explicit derivation was omitted. The revision will include a short thermodynamic subsection presenting the relevant Maxwell relation connecting Q(T,μ) to entropy, the finite-temperature corrections for the anyonic contribution, and a numerical estimate confirming that charge resolution of order 0.1e suffices to resolve k_B log √2. revision: yes

  3. Referee: [Proposal section (inferred from abstract)] The manuscript contains no error analysis, Monte-Carlo simulation of phase-to-charge conversion, or estimate of systematic offsets from non-equilibrium quasiparticle dynamics; without these, it is impossible to judge whether the O(1) entropy signal survives the measurement protocol.

    Authors: We accept that a quantitative error analysis is necessary. The revised version will contain an error-budget subsection that analytically estimates systematic offsets arising from non-equilibrium dynamics and phase-to-charge conversion, together with bounds showing that the O(1) entropy signal remains detectable. A full Monte-Carlo simulation lies outside the scope of this proposal-style manuscript, but the analytical estimates will allow readers to assess feasibility. revision: partial

Circularity Check

0 steps flagged

No circularity; proposal uses external experimental observations of phase switching

full rationale

The manuscript proposes extracting non-Abelian anyon entropy ΔS = k_B log d from equilibrium antidot charge Q(T,μ) via Maxwell relations, with Q inferred from time-dependent interference-phase switching reported in prior experiments. No equations or steps reduce the target entropy to a fitted parameter, self-citation, or ansatz internal to the paper. The temperature window and measurement scheme are presented as a proposal relying on external data rather than internal consistency conditions. No load-bearing self-citations or self-definitional relations appear in the provided abstract or described derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The proposal implicitly assumes standard quantum Hall edge theory and Maxwell relations hold for the antidot system.

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Reference graph

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