Quantum wires, Chern-Simons theory, and dualities in the quantum Hall system

TL;DR

This paper explores the connections between quantum wires, Chern-Simons theory, and dualities to provide a unified understanding of Laughlin states in the fractional quantum Hall system, bridging microscopic and macroscopic descriptions.

Contribution

It introduces a framework linking quantum wires, bosonization, and particle-vortex duality to derive effective field theories for quantum Hall states.

Findings

Derived 2+1D effective theories from 1+1D quantum wire models.

Demonstrated the role of gauge invariance and dualities in connecting microscopic and macroscopic descriptions.

Provided a unified approach to understanding fractional quantum Hall states.

Abstract

Over the years, many theoretical frameworks have been developed to understand the remarkable physics of the quantum Hall system. In this work we discuss the interplay among quantum wires, Chern-Simons theory, bosonization, and particle-vortex duality, which enable a unified approach for the Laughlin states of the fractional quantum Hall system. Starting from the so-called quantum wires system, which is a semi-microscopic description in terms of 1+1 dimensional theories, we discuss the emergence of 2+1 dimensional low-energy effective field theories by using different maps connecting the microscopic degrees of freedom with the macroscopic ones. We show the origin of these maps by embedding the bosonized version of the original quantum wires model in a gauge invariant theory and using particle vortex-duality.