# Hyperspherical Slater determinant approach to few-body fractional quantum Hall states

## Abstract

In a recent study (Daily et al., 2015), a hyperspherical approach has been developed to study few-body fractional quantum Hall states. This method has been successfully applied to the exploration of few boson and fermion problems in the quantum Hall region, as well as the study of inter-Landau level collective excitations (Rittenhouse et al., 2016; Wooten et al., 2016). However, the hyperspherical method as it is normally implemented requires a subsidiary (anti-)symmetrization process, which limits its computational effectiveness. The present work overcomes these difficulties and extends the power of this method by implementing a representation of the hyperspherical many-body basis space in terms of Slater determinants of single particle eigenfunctions. A clear connection between the hyperspherical representation and the conventional single particle picture is presented, along with a compact operator representation of the theoretical framework. - Highlights: • A hyperspherical method has been implemented to study the quantum Hall effect. • The hyperspherical many-body basis space is represented with Slater determinants. • Example numerical studies of the 4- and 8-electron systems are presented.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22617504

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 380; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSONS; EIGENFUNCTIONS; HALL EFFECT; MANY-BODY PROBLEM; NUMERICAL ANALYSIS; QUANTUM STATES; SLATER METHOD

### Citation Formats

```
Yan, Bin, E-mail: yanbin@purdue.edu, Wooten, Rachel E., Daily, Kevin M., and Greene, Chris H.
```*Hyperspherical Slater determinant approach to few-body fractional quantum Hall states*. United States: N. p., 2017.
Web. doi:10.1016/J.AOP.2017.03.004.

```
Yan, Bin, E-mail: yanbin@purdue.edu, Wooten, Rachel E., Daily, Kevin M., & Greene, Chris H.
```*Hyperspherical Slater determinant approach to few-body fractional quantum Hall states*. United States. doi:10.1016/J.AOP.2017.03.004.

```
Yan, Bin, E-mail: yanbin@purdue.edu, Wooten, Rachel E., Daily, Kevin M., and Greene, Chris H. Mon .
"Hyperspherical Slater determinant approach to few-body fractional quantum Hall states". United States.
doi:10.1016/J.AOP.2017.03.004.
```

```
@article{osti_22617504,
```

title = {Hyperspherical Slater determinant approach to few-body fractional quantum Hall states},

author = {Yan, Bin, E-mail: yanbin@purdue.edu and Wooten, Rachel E. and Daily, Kevin M. and Greene, Chris H.},

abstractNote = {In a recent study (Daily et al., 2015), a hyperspherical approach has been developed to study few-body fractional quantum Hall states. This method has been successfully applied to the exploration of few boson and fermion problems in the quantum Hall region, as well as the study of inter-Landau level collective excitations (Rittenhouse et al., 2016; Wooten et al., 2016). However, the hyperspherical method as it is normally implemented requires a subsidiary (anti-)symmetrization process, which limits its computational effectiveness. The present work overcomes these difficulties and extends the power of this method by implementing a representation of the hyperspherical many-body basis space in terms of Slater determinants of single particle eigenfunctions. A clear connection between the hyperspherical representation and the conventional single particle picture is presented, along with a compact operator representation of the theoretical framework. - Highlights: • A hyperspherical method has been implemented to study the quantum Hall effect. • The hyperspherical many-body basis space is represented with Slater determinants. • Example numerical studies of the 4- and 8-electron systems are presented.},

doi = {10.1016/J.AOP.2017.03.004},

journal = {Annals of Physics},

number = ,

volume = 380,

place = {United States},

year = {Mon May 15 00:00:00 EDT 2017},

month = {Mon May 15 00:00:00 EDT 2017}

}