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

Abstract Advancing a microscopic field-theoretic 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 such a 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 connection and perform Monte Carlo simulations that numerically confirm the fusion mechanism for quasiparticles. Thus, two quasiholes plus one electron leads to an exact quasielectron state of fractional charge e/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 in a manner that highlights the lack of local condensation. Furthermore, we present a rigorous constructive subspace bosonization dictionary for the bulk fluid and establish the universal long-distance behavior of edge excitations by formulating a conjecture based on the DNA, or root state, of the FQH fluid.