Journal
PHYSICAL REVIEW LETTERS
Volume 119, Issue 14, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.119.146602
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Funding
- Leo Kadanoff fellowship
- NSF [DMS-1206648]
- Simons Center for Geometry and Physics, Stony Brook University
- Banff International Research Station
- Department of Energy BES [DE-SC0002140]
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1206648] Funding Source: National Science Foundation
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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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