## SciPost Submission Page

# Microscopic derivation of Ginzburg-Landau theories for hierarchical quantum Hall states

### by Y. Tournois, M. Hermanns, T. H. Hansson

#### - Published as SciPost Phys. 8, 079 (2020)

### Submission summary

As Contributors: | Hans Hansson · Maria Hermanns · Yoran Tournois |

Arxiv Link: | https://arxiv.org/abs/2002.08711v2 |

Date accepted: | 2020-05-04 |

Date submitted: | 2020-04-24 |

Submitted by: | Tournois, Yoran |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Condensed Matter Physics - Theory |

Approach: | Theoretical |

### Abstract

We propose a Ginzburg-Landau theory for a large and important part of the abelian quantum Hall hierarchy, including the prominently observed Jain sequences. By a generalized "flux attachment" construction we extend the Ginzburg-Landau-Chern-Simons composite boson theory to states obtained by both quasielectron and quasihole condensation, and express the corresponding wave functions as correlators in conformal field theories. This yields a precise identification of the relativistic scalar fields entering these correlators in terms of the original electron field.

### Ontology / Topics

See full Ontology or Topics database.Published as SciPost Phys. 8, 079 (2020)

### List of changes

1. We added a comment on existing GLCS theories on page 4

2. We added a comment on page 17, emphasizing that the orbital spin is an input to our construction to correctly implement the topological data

3. We added a comment below Eq. 5 on the phase field

4. We fixed a broken reference on page 13, a wrong variable in the mean-field solution below Eq. 6, and we added hats to fields in Eqs. (20),(28) and (58)

5. We slightly modified the first footnote on page 8

6. We added two references

7. We fixed typos and grammar

8. We reformulated the explanation of the status of the field $\hat{\phi}$ around eq. (20) and after eq. (46).