Investigating anisotropic quantum Hall states with bi-metric geometry

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 bi-metric 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 (DMRG). 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.

v1. 5 pages, no figures v2. New title, added numerical results for viscosity of anisotropic systems. Now 5.5 pages + 2 page supplementary material, 1 figure. v3. Improved discussion in the main text, expanded supplementary material, and fixed typos. Now 5.5 pages + 5.5 page supplementary material. v4. Accepted version v5. Fixed missing reference

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