Unexpected non-universality of the time braiding phase of anyons tied by the scaling dimension

TL;DR

The paper investigates whether the time-domain braiding phase $θ$ of anyons is universal or encoded in edge dynamics. Using a braiding fluctuation-dissipation theorem within the Unified Non-equilibrium Perturbative Theory, it derives an integral equation relating DC noise to DC current and solves it analytically by a Wiener–Hopf method in the thermal Poisson-noise limit. It shows that the time-domain braiding phase is tied to the scaling dimension via $δ = θ/π - n$ (with $0<δ<1$), implying nonuniversality and that temporal braiding reflects nonuniversal edge physics except in special chiral-TLL limits. The results provide a practical route to extract $θ$ from DC transport and clarify the relation between time- and space-domain braiding in fractional quantum Hall edge states.

Abstract

We use a braiding nonequilibrium fluctuation dissipation relation linking the DC noise to the response function inferred from the braiding constraint in the time-domain with a phase $θ$ within the UNEPT (Unified Non equilibrium Perturbative Theory). By applying the Kramers-Krönig relations, we obtain an integral equation connecting DC current and noise that involves $θ$. By specifying to thermal states so that noise is Poissonian, we find an analytical solution for the DC current via the Wiener-Hopf technique. It reveals that the time-braiding phase is determined by the scaling dimension~$δ$. This questions the universality of $θ$ that can reflect the microscopic edge dynamics, in contrast to the topologically protected braiding phase in the space domain.

Figures (1)

• Figure 1: A QPC in the quantum Hall regime at an integer or fractional filling factor $\nu$. We focus here on edges such that each harbors only a single chiral mode. While $V_u$ and $V_d$ denote the reservoir voltages.