# Geometric response of quantum Hall states to electric fields

## TL;DR

This paper explores how non-uniform electric fields influence quantum Hall states by linking their response to the underlying quantum geometry, suggesting electric fields can mimic spatial curvature effects and involve gravitational coupling in charge responses.

## Contribution

It introduces a gauge-invariant geometric framework connecting electric field responses in quantum Hall states to spatial curvature and gravitational effects.

## Key findings

- Non-uniform electric fields mimic spatial curvature effects.
- Charge response involves gravitational coupling constant.
- Provides a geometric interpretation of quantum Hall responses.

## Abstract

Exploiting novel aspects of the quantum geometry of charged particles in a magnetic field via gauge-invariant variables, we provide tangible connections between the response of quantum Hall fluids to non-uniform electric fields and the characteristic geometry of electronic motion in the presence of magnetic and electric fields. The geometric picture we provide motivates the following conjecture: non-uniform electric fields mimic the presence of spatial curvature. Consequently, the gravitational coupling constant also appears in the charge response to non-uniform electric fields.