Fractional quantum Hall anyons: from Abelian to non-Abelian non-equilibrium bosonization.

• Applicant: Dr. Jinhong Park, Ph.D.
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 559260877

Two-dimensional systems may have exotic particles, the so-called anyons, which exhibit distinct exchange statistics from fermions and bosons; after exchanging two anyons, the wave function acquires a phase factor e^iθ, where the exchange phase θ differs from either 0 (boson) or π (fermion). Due to its fundamental and topological nature, the anyonic exchange statistics has brought tremendous attention to its experimental verification. The fractional quantum Hall (FQH) effect serves as a condensed-matter platform to possess anyons as elementary excitations. Remarkably, a plethora of FQH states have been observed. In particular, several FQH states at certain filling fractions are expected to have non-Abelian anyons, whose exchange statistics are encoded in a unitary matrix rather than a phase factor. These non-Abelian anyons have received attention due to their potential to serve as qubits for fault-tolerant quantum computation. Recent years have witnessed remarkable progress in detecting Abelian exchange anyons. An approach for detecting anyonic statistics is to impinge dilute edge-anyon beams onto a single quantum point contact (QPC) and to measure the tunneling current and the electrical noise through the QPC. Remarkably, the ratio of noise to tunneling current, the so-called Fano factor, reveals the anyonic statistics as demonstrated in experiments. While the experiment in the 1/3 state (the simplest Laughlin state) is fully consistent with a theoretical prediction, the measured Fano factors in hierarchical states involving complex edge structures significantly deviate from the theory, which calls for developing a theoretical framework for complex edges. Furthermore, a theoretical framework for non-Abelian anyons out of equilibrium is not yet established. The goal of this project is to develop a theoretical framework for Abelian and non-Abelian anyons out of equilibrium. The project aims to expand the current understanding of anyons in the Laughlin states to a broad class of FQH states with complex edge structures, in which multiple edge modes propagate with their respective propagation directions. This broad FQH class ranges from Abelian to non-Abelian states. I will first focus on Abelian anyons with exchange phase θ>π/2, which appear in complex edges. The effect of interactions and tunneling on spectral and transport properties will be further explored. This theoretical development will be extended to non-Abelian anyons. The general framework for non-Abelian anyons to be developed will be applied to various non-Abelian states, including main candidates of the 5/2 state and the Read-Rezayi states.

• DFG Programme: Research Grants
• International Connection: Sweden
• Cooperation Partner: Dr. Christian Spånslätt