Fractionalisation and dynamics of anyons at $\nu=n+1/3$ in fractional quantum Hall effect and their experimental signatures

TL;DR

This paper explores the fractionalization and dynamics of anyons at specific filling factors in the fractional quantum Hall effect, revealing new quasihole structures, their interactions, and potential experimental signatures of phase transitions.

Contribution

It introduces a novel understanding of quasiholes as bound states of Gaffnian quasiholes with rich dynamical properties and predicts a finite temperature phase transition.

Findings

Quasiholes can be viewed as bound states of Gaffnian quasiholes.

Weak binding and fractionalization occur near nematic FQH phases.

A finite temperature phase transition of Laughlin quasiholes is predicted.

Abstract

We show the low-lying excitations at filling factor $\nu=n+1/3$ with realistic interactions are contained completely within the well-defined Hilbert space of "Gaffnian quasiholes". Each Laughlin quasihole can thus be understood as a bound state of two Gaffnian quasiholes, which in the lowest Landau level (LLL) behaves like "partons" with "asymptotic freedom" mediated by neutral excitations acting as "gluons". Near the experimentally observed nematic FQH phase in higher LLs, quasiholes become weakly bounded and fractionalise with rich dynamical properties. By studying the effective interactions between quasiholes, we predict a finite temperature phase transition of the Laughlin quasiholes even when the Laughlin ground state remains incompressible, and derive relevant experimental conditions for its possible observations.