Investigating Anisotropic Quantum Hall States with Bimetric Geometry

Andrey Gromov, Scott D. Geraedts, Barry Bradlyn

Research output: Contribution to journalArticlepeer-review

Abstract

We construct a low energy effective theory of anisotropic fractional quantum Hall (FQH) states. We develop a formalism similar to that used in the bimetric approach to massive gravity, and apply it to describe Abelian anisotropic FQH states in the presence of external electromagnetic and geometric backgrounds. We derive a relationship between the shift, the Hall viscosity, and a new quantized coupling to anisotropy, which we term anisospin. We verify this relationship by numerically computing the Hall viscosity for a variety of anisotropic quantum Hall states using the density matrix renormalization group. Finally, we apply these techniques to the problem of nematic order and clarify certain disagreements that exist in the literature about the meaning of the coefficient of the Berry phase term in the nematic effective action.

Original languageEnglish (US)
Article number146602
JournalPhysical review letters
Volume119
Issue number14
DOIs
StatePublished - Oct 5 2017
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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