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

### Submission summary

 As Contributors: Hans Hansson · Maria Hermanns · Yoran Tournois Arxiv Link: https://arxiv.org/abs/2002.08711v2 (pdf) Date accepted: 2020-05-04 Date submitted: 2020-04-24 02:00 Submitted by: Tournois, Yoran Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Quantum Physics 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

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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).