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arxiv: 2606.10259 · v1 · pith:IZILY6PVnew · submitted 2026-06-08 · ❄️ cond-mat.str-el

Coherent manipulation of Kondo Majoranas in two-channel Kondo setups

Yashar Komijani , C. J. Bolech This is my paper

Pith reviewed 2026-06-27 14:29 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords Kondo Majoranastwo-channel KondoMajorana zero modesnon-Abelian anyonsY-junction geometrybraiding operationsgeometric holonomy
0
0 comments X

The pith

Two-channel Kondo systems host interacting Majorana modes that enable non-local qubits and braiding in topological Y-junctions.

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

The paper examines Majorana zero modes that emerge in overscreened two-channel Kondo systems. Using compactified lattice models, the authors show that these interacting modes support non-local qubits and permit teleportation, fusion, and braiding. They distinguish non-topological from genuinely topological Y-junction geometries, where only the latter produces non-Abelian geometric holonomy. The work supplies a proof-of-principle path for coherent control of non-Abelian anyons outside standard free-fermion platforms.

Core claim

Using compactified lattice models, we show that interacting Kondo Majoranas support non-local qubits and admit teleportation, fusion, and braiding operations. In particular, we identify a distinction between non-topological and genuinely topological Y-junction geometries, the latter realizing a non-Abelian geometric holonomy. Our results establish a proof-of-principle route toward coherent control of non-Abelian anyons beyond conventional free-fermion platforms.

What carries the argument

Compactified lattice models of overscreened two-channel Kondo systems that distinguish genuinely topological Y-junction geometries and the non-Abelian geometric holonomy they produce.

If this is right

  • The modes form non-local qubits.
  • Teleportation, fusion, and braiding operations become admissible.
  • Only genuinely topological Y-junctions produce non-Abelian geometric holonomy.
  • A route opens to coherent control of non-Abelian anyons in interacting platforms.

Where Pith is reading between the lines

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

  • Device designs based on Kondo quantum dots or nanowires could target the topological Y-junction geometries.
  • The same modeling approach may apply to other overscreened Kondo realizations for similar topological features.
  • The geometric distinction supplies a concrete criterion for engineering non-Abelian behavior in lattice-based setups.

Load-bearing premise

The compactified lattice models accurately capture the physics of overscreened two-channel Kondo systems and allow identification of genuinely topological versus non-topological geometries without additional assumptions about interactions or disorder.

What would settle it

An experiment on a Y-junction geometry predicted to be topological that fails to show non-Abelian geometric holonomy, or one on a predicted non-topological geometry that does show it, would falsify the central distinction.

Figures

Figures reproduced from arXiv: 2606.10259 by C. J. Bolech, Yashar Komijani.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) [41]. In all cases, we initialize two detached Kondo MZMs on the x and y legs and perform the cyclic transfer sequence y → z, x → y, and z → x, thereby exchanging the two Kondo anyons [ [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

We study coherent manipulation of Majorana zero modes emerging in overscreened two-channel Kondo systems. Using compactified lattice models, we show that these interacting Kondo Majoranas support non-local qubits and admit teleportation, fusion, and braiding operations. In particular, we identify a distinction between non-topological and genuinely topological Y-junction geometries, the latter realizing a non-Abelian geometric holonomy. Our results establish a proof-of-principle route toward coherent control of non-Abelian anyons beyond conventional free-fermion platforms.

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

1 major / 1 minor

Summary. The manuscript studies coherent manipulation of Majorana zero modes in overscreened two-channel Kondo systems using compactified lattice models. It claims that these interacting Kondo Majoranas enable non-local qubits and operations including teleportation, fusion, and braiding. A key result is the distinction between non-topological and genuinely topological Y-junction geometries, where the latter realizes a non-Abelian geometric holonomy, providing a proof-of-principle for coherent control of non-Abelian anyons beyond free-fermion platforms.

Significance. If the central claims hold under the compactified models, the work would establish a new interacting platform for non-Abelian anyon operations, extending beyond conventional free-fermion Majorana systems and offering a route to coherent control in Kondo setups.

major comments (1)
  1. [Y-junction geometries section] The distinction between non-topological and genuinely topological Y-junction geometries (and the associated non-Abelian geometric holonomy) is load-bearing for the central claim. The manuscript relies on compactified lattice models to capture the overscreened two-channel Kondo fixed point and to differentiate the geometries, but provides no explicit robustness checks against continuum limits, finite-size gaps, channel asymmetry, or irrelevant operators that could mask or alter the distinction.
minor comments (1)
  1. Ensure that all numerical or simulation parameters used in the lattice models are fully specified to allow reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for recognizing the potential significance of the results on coherent manipulation of Kondo Majoranas. We address the single major comment below.

read point-by-point responses

  1. Referee: [Y-junction geometries section] The distinction between non-topological and genuinely topological Y-junction geometries (and the associated non-Abelian geometric holonomy) is load-bearing for the central claim. The manuscript relies on compactified lattice models to capture the overscreened two-channel Kondo fixed point and to differentiate the geometries, but provides no explicit robustness checks against continuum limits, finite-size gaps, channel asymmetry, or irrelevant operators that could mask or alter the distinction.

    Authors: We agree that the distinction between the Y-junction geometries is central and that explicit robustness checks would strengthen the presentation. The compactified lattice models are constructed to realize the overscreened two-channel Kondo fixed point exactly in the infrared while preserving the lattice connectivity needed to define the junctions; the non-Abelian holonomy then follows from the symmetry-protected effective Majorana Hamiltonian. Finite-size gaps are controlled by the system sizes employed (with the Kondo scale setting the gap), channel asymmetry is irrelevant at the fixed point, and irrelevant operators are suppressed under renormalization. Nevertheless, the manuscript does not contain dedicated scans or extrapolations addressing continuum limits or operator perturbations. In the revised version we will add a dedicated paragraph in the Y-junction section that (i) recalls the RG irrelevance of the listed perturbations at the 2CK fixed point and (ii) provides a brief numerical check of the holonomy under moderate channel asymmetry within the lattice model. revision: partial

Circularity Check

0 steps flagged

No circularity; derivation relies on explicit lattice model simulations without reduction to inputs by construction

full rationale

The provided abstract and context contain no equations, self-referential definitions, fitted parameters renamed as predictions, or load-bearing self-citations. The central claims about non-local qubits, teleportation, fusion, braiding, and distinction between Y-junction geometries are presented as results obtained from compactified lattice models of overscreened two-channel Kondo systems. No step reduces the output to the input by definition or statistical forcing, and the derivation chain appears self-contained against the model's explicit construction rather than tautological. This is the expected outcome for a paper whose results are generated from numerical or analytical treatment of a defined Hamiltonian without circular renaming or imported uniqueness theorems.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities; full text would be needed to audit model assumptions or lattice compactification details.

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Reference graph

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