Quantum Hall hierarchy from coupled wires

TL;DR

This paper develops a coupled-wire framework to model various hierarchical quantum Hall states, including Jain, Haldane-Halperin, and Moore-Read states, revealing new insights into their structure and symmetries.

Contribution

It introduces a versatile coupled-wire construction that captures hierarchical quantum Hall phenomenologies and connects different states through flux attachment, vortex duality, and particle-hole symmetry.

Findings

Unified coupled-wire models for Jain and Haldane-Halperin hierarchies

Explicit connection between Moore-Read state and p-wave pairing

Compatibility of models with particle-hole symmetry at ν=1/2

Abstract

The coupled-wire construction provides a useful way to obtain microscopic Hamiltonians for various two-dimensional topological phases, among which fractional quantum Hall states are paradigmatic examples. Using the recently introduced flux attachment and vortex duality transformations for coupled wires, we show that this construction is remarkably versatile to encapsulate phenomenologies of hierarchical quantum Hall states: the Jain-type hierarchy states of composite fermions filling Landau levels and the Haldane-Halperin hierarchy states of quasiparticle condensation. The particle-hole conjugate transformation for coupled-wire models is also given as a special case of the hierarchy construction. We also propose coupled-wire models for the composite Fermi liquid, which turn out to be compatible with a sort of the particle-hole symmetry implemented in a nonlocal way at $\nu=1/2$. Furthermore, our approach shows explicitly the connection between the Moore-Read Pfaffian state and a chiral $p$-wave pairing of the composite fermions. This composite fermion picture is also generalized to a family of the Pfaffian state, including the anti-Pfaffian state and Bonderson-Slingerland hierarchy states.