Galilean invariance at quantum Hall edge

TL;DR

This paper develops a Galilean invariant chiral Luttinger liquid theory for quantum Hall edges, enabling new insights into electromagnetic responses and potential experimental measurements of bulk properties.

Contribution

It introduces a Galilean invariant boundary theory for quantum Hall fluids, ensuring total system invariance and linking edge responses to bulk Hall viscosity.

Findings

Derived momentum- and frequency-dependent electric conductivity at the edge.

Proposed experimental method to measure bulk Hall viscosity.

Established a Galilean invariant framework for quantum Hall edge dynamics.

Abstract

We construct the theory of a chiral Luttinger liquid that lives on the boundary of a Galilean invariant quantum Hall fluid. In contrast to previous studies, Galilean invariance of the total (bulk plus edge) theory is guaranteed. We consider electromagnetic response at the edge and calculate momentum- and frequency-dependent electric conductivity and argue that its experimental measurement can provide a new means to determine the shift and bulk Hall viscosity.