A Typology for Quantum Hall Liquids

TL;DR

This paper introduces a detailed classification system for quantum Hall liquids based on their response to density changes, drawing analogies with superconductors and highlighting the rich variety of quantum Hall phases.

Contribution

It develops a new typology for quantum Hall liquids using the Chern-Simons Landau-Ginzburg framework, including the concept of a Bogomol'nyi point and its implications.

Findings

Different types of QHLs can produce quantized Hall plateaux.

The boundary between Type I and Type II QHLs features a non-interacting vortex point.

The classification extends the analogy with superconductors to a richer set of behaviors.

Abstract

There is a close analogy between the response of a quantum Hall liquid (QHL) to a small change in the electron density and the response of a superconductor to an externally applied magnetic flux - an analogy which is made concrete in the Chern-Simons Landau-Ginzburg (CSLG) formulation of the problem. As the Types of superconductor are distinguished by this response, so too for QHLs: a typology can be introduced which is, however, richer than that in superconductors owing to the lack of any time-reversal symmetry relating positive and negative fluxes. At the boundary between Type I and Type II behavior, the CSLG action has a "Bogomol'nyi point," where the quasi-holes (vortices) are non-interacting - at the microscopic level, this corresponds to the behavior of systems governed by a set of model Hamiltonians which have been constructed to render exact a large class of QHL wavefunctions. All Types of QHLs are capable of giving rise to quantized Hall plateaux.