Geometry of flux attachment in anisotropic fractional quantum Hall states

TL;DR

This paper investigates how the internal geometric metric of fractional quantum Hall states responds to anisotropy, revealing sequence-dependent behavior and providing a microscopic explanation for flux attachment effects.

Contribution

It introduces a method to extract the internal metric from structure factors and explains the anisotropic response in terms of flux attachment models.

Findings

Response to anisotropy is similar within the same Jain sequence.

Response varies significantly between different sequences.

Provides a microscopic flux attachment model explaining the behavior.

Abstract

Fractional quantum Hall (FQH) states are known to possess an internal metric degree of freedom that allows them to minimize their energy when contrasting geometries are present in the problem (e.g., electron band mass and dielectric tensor). We investigate the internal metric of several incompressible FQH states by probing its response to band mass anisotropy using infinite DMRG simulations on a cylinder geometry. We test and apply a method to extract the internal metric of a FQH state from its guiding center structure factor. We find that the response to band mass anisotropy is approximately the same for states in the same Jain sequence, but changes substantially between different sequences. We provide a theoretical explanation of the observed behavior of primary states at filling $\nu = 1/m$ in terms of a minimal microscopic model of flux attachment.