On the edge of certain fractional quantum Hall states, e.g., at 2/3 and 5/2 filling, a local fractional excitation, occurring by anyon tunneling at a quantum point contact, is further fractionalized into counterpropagating charge and neutral (Abelian or non-Abelian) anyonic excitations. We propose a scheme to detect the braiding statistics of the charge and neutral anyons separately. It is the injection of a dilute beam of a target (charge or neutral) anyon to a Fabry-Perot interferometer. The monodromy of the target anyon is obtained by comparing the amplitude and phase of the interference current with a reference signal of the same setup but without the injection. Our proposal relies on braiding between anyons on the edge, and applies even in the presence of bulk-edge couplings.On the edge of certain fractional quantum Hall states, e.g., at 2/3 and 5/2 filling, a local fractional excitation, occurring by anyon tunneling at a quantum point contact, is further fractionalized into counterpropagating charge and neutral (Abelian or non-Abelian) anyonic excitations. We propose a scheme to detect the braiding statistics of the charge and neutral anyons separately. It is the injection of a dilute beam of a target (charge or neutral) anyon to a Fabry-Perot interferometer. The monodromy of the target anyon is obtained by comparing the amplitude and phase of the interference current with a reference signal of the same setup but without the injection. Our proposal relies on braiding between anyons on the edge, and applies even in the presence of bulk-edge couplings.

Physical Review LettersOct 29, 20240 citations

Edge Excitations of Quantum Hall States

WORLD SCIENTIFIC eBooksApr 1, 20230 citations

Lattice spin models for non-Abelian chiral spin liquids

P. Lecheminant, Alexei M. Tsvelik

We suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids---spin analogs of fractional non-Abelian quantum Hall states---with gapped bulk and gapless chiral edge excitations described by the SU(2) ${}_{n}$ Wess-Zumino-Novikov-Witten conformal field theory. The models are constructed from an array of generalized spin- $n/2$ ladders with multi-spin-exchange interactions which are coupled by isolated spins. Such models allow a controllable analytic treatment starting from the one-dimensional limit and are characterized by a bulk gap and non-Abelian SU(2) ${}_{n}$ gapless edge excitations.We suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids---spin analogs of fractional non-Abelian quantum Hall states---with gapped bulk and gapless chiral edge excitations described by the SU(2)${}_{n}$ Wess-Zumino-Novikov-Witten conformal field theory. The models are constructed from an array of generalized spin-$n/2$ ladders with multi-spin-exchange interactions which are coupled by isolated spins. Such models allow a controllable analytic treatment starting from the one-dimensional limit and are characterized by a bulk gap and non-Abelian SU(2)${}_{n}$ gapless edge excitations.

arXiv:1608.05977Physical review. B./Physical review. BApr 26, 201739 citations

Transport theory for a generic two-arm co-propagating Majorana interferometer with Majorana fermion and edge vortex tunneling

Domenico Giuliano, Andrea Nava, Fabian Hassler +1 more

Co-propagating chiral Majorana edge modes are predicted to exist in proximity-coupled quantum anomalous Hall systems. They combine the exciting prospects of edge vortices as flying non-Abelian Ising anyons, with their fully electrical detection through anyon fusion processes. In this setup, electrical transport arises from the interference of a pair of Majorana edge states. By bosonizing the model with an additional replica sector, we generalize previous treatments to fully asymmetric configurations. We analyze a Mach-Zehnder interferometer and show that while the DC conductance does not exhibit signatures of edge-vortex interference, at low frequencies, this interference manifests as an effective capacitance. This quantity is sensitive to the non-Abelian anyon statistics of edge vortices and, in particular, carries signatures of their topological spin and nontrivial conformal dimension. We demonstrate that the thermal length $l_T = \hbar v/(πk_B T)$ is the relevant scale at low temperatures $T$ , analogous to quasiparticle transport in conventional quantum Hall edge states with velocity $v$ . As long as the interferometer arm lengths match within this length scale, transport signatures of the non-Abelian statistics of edge vortices remain visible.Co-propagating chiral Majorana edge modes are predicted to exist in proximity-coupled quantum anomalous Hall systems. They combine the exciting prospects of edge vortices as flying non-Abelian Ising anyons, with their fully electrical detection through anyon fusion processes. In this setup, electrical transport arises from the interference of a pair of Majorana edge states. By bosonizing the model with an additional replica sector, we generalize previous treatments to fully asymmetric configurations. We analyze a Mach-Zehnder interferometer and show that while the DC conductance does not exhibit signatures of edge-vortex interference, at low frequencies, this interference manifests as an effective capacitance. This quantity is sensitive to the non-Abelian anyon statistics of edge vortices and, in particular, carries signatures of their topological spin and nontrivial conformal dimension. We demonstrate that the thermal length $l_T = \hbar v/(πk_B T)$ is the relevant scale at low temperatures $T$, analogous to quasiparticle transport in conventional quantum Hall edge states with velocity $v$. As long as the interferometer arm lengths match within this length scale, transport signatures of the non-Abelian statistics of edge vortices remain visible.

cond-mat.mes-hallCross-listedarXiv:2610.01402Oct 2, 2026

Non-abelian Quantum Hall States on the

Thin Torus

Jan 1, 20090 citations

Dynamics, interferometry and fractional statistics of bulk Quantum Hall coherent states

Varsha Subramanyan, Smitha Vishveshwara

Bulletin of the American Physical SocietyMar 6, 20180 citations

Exact Solution for Bulk-Edge Coupling in the Non-Abelian

\nu=5/2

Quantum Hall Interferometer

{}_{n}

Wess-Zumino-Novikov-Witten conformal field theory. The models are constructed from an array of generalized spin-

n/2

ladders with multi-spin-exchange interactions which are coupled by isolated spins. Such models allow a controllable analytic treatment starting from the one-dimensional limit and are characterized by a bulk gap and non-Abelian SU(2)

{}_{n}

gapless edge excitations.

l_T = \hbar v/(πk_B T)

is the relevant scale at low temperatures

T

, analogous to quasiparticle transport in conventional quantum Hall edge states with velocity

v

. As long as the interferometer arm lengths match within this length scale, transport signatures of the non-Abelian statistics of edge vortices remain visible.