Electromagnetic response and effective gauge theory of double-layer quantum Hall systems

TL;DR

This paper develops an effective gauge theory for double-layer quantum Hall systems using bosonization, emphasizing the role of dipole-active excitations and response functions, and critically examines standard Chern-Simons approaches.

Contribution

It introduces a new gauge theory derived from response functions without composite particles, highlighting the importance of dipole-active modes in quantum Hall systems.

Findings

Effective theory includes three vector fields for collective and cyclotron modes.

Long-wavelength features are governed by dipole-active excitations.

Critically analyzes limitations of standard Chern-Simons theories.

Abstract

We report on an effective gauge theory of double-layer quantum Hall systems, that is constructed via bosonization from the response of incompressible states without referring to composite bosons and fermions. It is pointed out that dipole-active excitations, both elementary and collective, govern the long-wavelength features of quantum Hall systems, and the single-mode approximation is used to study them. The effective theory consists of three vector fields representing one interlayer collective mode and two cyclotron modes, and properly incorporates the spectrum of collective excitations on the right scale of the Coulomb interaction. Special emphasis is placed on exploring the advantage of looking into quantum Hall systems through their response; in particular, subtleties inherent to the standard Chern-Simons theories are critically examined.