# The Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect

## Abstract

This paper gives a systematic review of a field theoretical approach to the fractional quantum Hall effect (FQHE) that has been developed in the past few years. The authors first illustrate some simple physical ideas to motivate such an approach and then present a systematic derivation of the Chern-Simons-Landau-Ginzburg (CSLG) action for the FQHE, starting from the microscopic Hamiltonian. It is demonstrated that all the phenomenological aspects of the FQHE can be derived from the mean field solution and the small fluctuations of the CSLG action. Although this formalism is logically independent of Laughlin's wave function approach, their physical consequences are equivalent. In particular, it is shown that the Laughlin's wave function can be derived from the CSLG theory under reasonable approximations. The CSLG theory demonstrates a deep connection between the phenomena of superfluidity and the FQHE, and can provide a simple and direct formalism to address many new macroscopic phenomena of the FQHE.

- Authors:

- (IBM Research Div., Almaden Research Center, San Jose, CA (US))

- Publication Date:

- OSTI Identifier:
- 5223253

- Alternate Identifier(s):
- OSTI ID: 5223253

- Resource Type:
- Journal Article

- Journal Name:
- International Journal of Modern Physics B; (United States)

- Additional Journal Information:
- Journal Volume: 6:5; Journal ID: ISSN 0217-9792

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; HALL EFFECT; QUANTIZATION; FIELD THEORIES; GINZBURG-LANDAU THEORY; HAMILTONIANS; NONLINEAR PROBLEMS; REVIEWS; DOCUMENT TYPES; MATHEMATICAL OPERATORS; QUANTUM OPERATORS 665411* -- Basic Superconductivity Studies-- (1992-); 662110 -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)

### Citation Formats

```
Zhang, S.C.
```*The Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect*. United States: N. p., 1992.
Web. doi:10.1142/S0217979292000499.

```
Zhang, S.C.
```*The Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect*. United States. doi:10.1142/S0217979292000499.

```
Zhang, S.C. Sun .
"The Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect". United States. doi:10.1142/S0217979292000499.
```

```
@article{osti_5223253,
```

title = {The Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect},

author = {Zhang, S.C.},

abstractNote = {This paper gives a systematic review of a field theoretical approach to the fractional quantum Hall effect (FQHE) that has been developed in the past few years. The authors first illustrate some simple physical ideas to motivate such an approach and then present a systematic derivation of the Chern-Simons-Landau-Ginzburg (CSLG) action for the FQHE, starting from the microscopic Hamiltonian. It is demonstrated that all the phenomenological aspects of the FQHE can be derived from the mean field solution and the small fluctuations of the CSLG action. Although this formalism is logically independent of Laughlin's wave function approach, their physical consequences are equivalent. In particular, it is shown that the Laughlin's wave function can be derived from the CSLG theory under reasonable approximations. The CSLG theory demonstrates a deep connection between the phenomena of superfluidity and the FQHE, and can provide a simple and direct formalism to address many new macroscopic phenomena of the FQHE.},

doi = {10.1142/S0217979292000499},

journal = {International Journal of Modern Physics B; (United States)},

issn = {0217-9792},

number = ,

volume = 6:5,

place = {United States},

year = {1992},

month = {3}

}