SciPost Submission Page
Multichannel topological Kondo models and their low-temperature conductances
by Guangjie Li, Elio J. König, Jukka I. Väyrynen
Submission summary
| Authors (as registered SciPost users): | Guangjie Li |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202508_00020v1 (pdf) |
| Date accepted: | Nov. 5, 2025 |
| Date submitted: | Aug. 6, 2025, 10:02 p.m. |
| Submitted by: | Guangjie Li |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In the multichannel Kondo effect, overscreening of a magnetic impurity by conduction electrons leads to a frustrated exotic ground state. It has been proposed that multichannel topological Kondo (MCTK) model involving topological Cooper pair boxes with M Majorana modes [SO(M) "spin"] and N spinless electron channels exhibits an exotic intermediate coupling fixed point. This intermediate fixed point has been analyzed through large-N perturbative calculations, which gives a zero-temperature conductance decaying as 1/N2 in the large-N limit. However, the conductance at this intermediate fixed point has not been calculated for generic N. Using representation theory, we verify the existence of this intermediate-coupling fixed point and find the strong-coupling effective Hamiltonian for the case M=4. Using conformal field theory techniques for SO(M), we generalize the notion of overscreening and conclude that the MCTK model is an overscreened Kondo model. We find the fixed-point finite-size energy spectrum and the leading irrelevant operator (LIO). We express the fixed-point conductance in terms of the modular S-matrix of SO(M) for general N, confirming the previous large-N result. We describe the finite-temperature corrections to the conductance by the LIO and find that they are qualitatively different for the cases N=1 and N≥2 due to the different fusion outcomes with the current operator. We also compare the multichannel topological Kondo model to the topological symplectic Kondo model.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
Reports on this Submission
Strengths
Rigorous application of conformal field theory techniques.
Weaknesses
Report
Requested changes
The authors can specify below Eq.16 the value of the central charge of each theory ($SO(M)_{2N}$ and $SO(2N)_{M}$) and check that it adds up to the correct total central charge.
Optional: The authors could write the non-abelian decomposition of the electron operator $(\psi_{n,\alpha} ,\psi^\dagger_{n,\alpha}) $ using their conformal embedding, into various representations of the above symmetries, checking that the scaling dimensions of these pieces add up correctly to the free electron scaling dimension 1/2.
The multiplicities in table II are all unity. Is this a typo? (what about degeneracies associated with the number of channels, particle-hole and $SO(M)$ symmetries?)
The authors stress (for example in Eq.3 or below Eq.11) that the two Majorana components of the leads add up, to yield an $SO(M)_2$ theory for $N=1$ and $SO(M)_{2N}$ for general $N$. Optional: Given that this work also provides an excellent account for literature, the authors can point out that in principle this symmetry can be broken down to $SO(M)_1$, as in Phys. Rev. B 95, 035135 (2017).
Using their explicit CFT construction, the authors carefully point out that in some cases, the leading finite-temperature correction arises at second order rather than first order. Optional: To clarify the connection with previous work, they could note that this detail was overlooked in the early Ref. 43, highlighting the importance of a careful CFT analysis to determine the temperature dependence.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Strengths
Weaknesses
Report
I think that the paper meets all the necessary criteria. It is valid and valuable (the SO(N) and Sp(2k) Kondo models are certainly of interest), it is probably not too original since it uses standard methods of CFT, it is exceedingly clear and pedagogical, very well formatted and, as far as I can judge, well written.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)