Zero Mode Operators and Charge-Conjugation Defects in Non-Abelian Fractional Quantum Hall-Superconductor Heterostructures

@misc{cao2026zero,
  title = {{Zero Mode Operators and Charge-Conjugation Defects in Non-Abelian Fractional Quantum Hall-Superconductor Heterostructures}},
  author = {Junyi Cao and Eduardo Fradkin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08907},
  eprint = {2610.08907},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08907},
}

TY  - UNPB
TI  - Zero Mode Operators and Charge-Conjugation Defects in Non-Abelian Fractional Quantum Hall-Superconductor Heterostructures
AU  - Junyi Cao
AU  - Eduardo Fradkin
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08907
UR  - https://arxiv.org/abs/2610.08907
AB  - We study zero modes bound to charge-conjugation defects in fractional quantum Hall-superconductor (FQH-SC) heterostructures built from Abelian and non-Abelian FQH states. Although the associated defects are well described by G-crossed braided tensor categories, a local operator description of their zero modes is not generally known. We generalize the bulk-to-boundary construction of localized zero mode operators to FQH-SCs with non-Abelian parent topological orders, mapping bulk Wilson operators in the folded theory to localized zero mode operators in the one-dimensional FQH-SC theory. This construction distinguishes zero mode anyons from the local zero mode operators that act on the defect Hilbert space and yields a generalized zero mode algebra. It also determines the fusion-channel dependence of tunneling: tunneling of zero mode operators probes bulk monodromy, while direct zero mode anyon transfer probes G-crossed associativity data. Applying this framework, we recover the ℤ_2m parafermion zero mode structure of fermionic Laughlin FQH-SCs at filling ν=1/m, obtain a ℤ_2^(n)×ℤ_N structure for generalized Moore-Read states at filling ν=1/m, with N=2m for fermionic states and N=m for bosonic states, and find a Fib×ℤ_N structure for the k=3 Read-Rezayi state at filling ν=3/(3M+2), with N=2(3M+2) for fermionic states and N=(3M+2)/2 for bosonic states. In the Read-Rezayi case, zero mode operator tunneling and direct zero mode anyon transfer yield distinct universal amplitude ratios between the neutral fusion channels, providing a characteristic signature of the underlying Fibonacci defect structure.
ER  -