# Single-mode approximation and effective Chern-Simons theories for quantum Hall systems

Source: [Single-mode approximation and effective Chern-Simons theories for quantum Hall systems](<https://www.sota2.com/research/paper/68fa26172c2a3760193b67a2>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T11:08:35.275Z

Authors: K. Shizuya

Published: 2003-06-20T10:38:26.000Z

## Abstract

A unified description of elementary and collective excitations in quantum Hall systems is presented within the single-mode approximation (SMA) framework, with emphasis on revealing an intimate link with Chern-Simons theories. It is shown that for a wide class of quantum Hall systems the SMA in general yields, as an effective theory, a variant of the bosonic Chern-Simons theory. For single-layer systems the effective theory agrees with the standard Chern-Simons theory at long wavelengths whereas substantial deviations arise for collective excitations in bilayer systems. It is suggested, in particular, that Hall-drag experiments would be a good place to detect out-of-phase collective excitations inherent to bilayer systems. It is also shown that the intra-Landau-level modes bear a similarity in structure (though not in scale) to the inter-Landau-level modes, and its implications on the composite-fermion and composite-boson theories are discussed.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0306524>)

[PDF](<https://arxiv.org/pdf/cond-mat/0306524.pdf>)