How Irrelevant Operators affect the Determination of Fractional Charge

TL;DR

This paper investigates how irrelevant operators in the Hamiltonian influence the measurement of fractional charge in quantum Hall systems, revealing non-perturbative effects that could explain experimental anomalies.

Contribution

It demonstrates that irrelevant terms can significantly alter charge measurements, challenging standard perturbative predictions in fractional quantum Hall edge tunneling.

Findings

Irrelevant operators cause non-perturbative behaviors in charge determination.

Effective measured charge can vary between $ u e$ and $e$ depending on conditions.

Results may explain previously unexplained experimental observations.

Abstract

We show that the inclusion of irrelevant terms in the Hamiltonian describing tunneling between edge states in the fractional quantum Hall effect can lead to a variety of non perturbative behaviors in intermediate energy regimes, and, in particular, affect crucially the determination of charge through shot noise measurements. We show, for instance, that certain combinations of relevant and irrelevant terms can lead to an effective measured charge $\nu e$ in the strong backscattering limit and an effective measured charge $e$ in the weak backscattering limit, in sharp contrast with standard perturbative expectations. This provides a possible scenario to explain the experimental observations by Heiblum and coworkers, which are so far not understood.