Mechanism for particle fractionalization and universal edge physics in quantum Hall fluids

TL;DR

This paper introduces a second-quantization framework that precisely explains particle fractionalization, topological order, and edge physics in fractional quantum Hall fluids, supported by analytic calculations and numerical simulations.

Contribution

It provides the first exact analytic computation of quasielectron properties and a rigorous bosonization dictionary for FQH fluids, revealing the underlying fusion mechanism and universal edge behavior.

Findings

Exact quasielectron charge and statistics computed analytically

Numerical confirmation of the fusion mechanism for quasiparticles

Universal long-distance edge excitation behavior established

Abstract

Advancing a microscopic framework that rigorously unveils the underlying topological hallmarks of fractional quantum Hall (FQH) fluids is a prerequisite for making progress in the classification of strongly-coupled topological matter. Here we advance a second-quantization framework that helps reveal an exact fusion mechanism for particle fractionalization in FQH fluids, and uncover the fundamental structure behind the condensation of non-local operators characterizing topological order in the lowest-Landau-level (LLL). We show the first exact analytic computation of the quasielectron Berry connections leading to its fractional charge and exchange statistics, and perform Monte Carlo simulations that numerically confirm the fusion mechanism for quasiparticles. Thus, for instance, two quasiholes plus one electron of charge $e$ lead to an exact quasielectron of fractional charge $e/3$, and exchange statistics $1/3$, in a $\nu=1/3$ Laughlin fluid. We express, in a compact manner, the sequence of (both bosonic and fermionic) Laughlin second-quantized states highlighting the lack of local condensation. Furthermore, we present a rigorous constructive subspace bosonization dictionary for the bulk fluid and establish universal long-distance behavior of edge excitations by formulating a conjecture based on the DNA, or root state, of the FQH fluid.