Geometry of flux attachment in anisotropic fractional quantum Hall states*

We study the internal metric of fractional quantum Hall (FQH) states, a degree of freedom which allows them to variationally optimize their energy in the presence of competing geometries. In particular, we focus on incompressible FQH states in the presence of isotropic Coulomb interaction and anisotropic band mass [1]. We use an infinite-cylinder density matrix renormalization group method [2] to numerically simulate these states and access their internal metric through the long-wavelength limit of their static guiding center structure factor. We find the response to band mass anisotropy is approximately the same for all states belonging to the first Jain sequence (ν = 1/3, 2/5, …). The ν = 1/5 state, on the other hand, exhibits markedly smaller anisotropy. The observed behavior is well captured by a two-body model of flux attachment.

[1] M. Ippoliti, R. N. Bhatt and F. D. M. Haldane, Phys. Rev. B 98, 085101 (2018).
[2] M. P. Zaletel et al., Phys. Rev. B 91, 045115 (2015).