Investigating Anisotropic Quantum Hall States with Bimetric Geometry

Gromov, Andrey; Geraedts, Scott D.; Bradlyn, Barry

doi:10.1103/physrevlett.119.146602

Title: Investigating Anisotropic Quantum Hall States with Bimetric Geometry

Journal Article · Thu Oct 05 00:00:00 EDT 2017 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.119.146602· OSTI ID:1541231

Gromov, Andrey ^[1]; Geraedts, Scott D. ^[2]; Bradlyn, Barry ^[3]

Univ. of Chicago, IL (United States). Kadanoff Center for Theoretical Physics
Princeton Univ., NJ (United States). Dept. of Electrical Engineering
Princeton Univ., NJ (United States). Princeton Center for Theoretical Science

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.

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Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0002140

OSTI ID:: 1541231

Alternate ID(s):: OSTI ID: 1398152

Journal Information:: Physical Review Letters, Vol. 119, Issue 14; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 33 works

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