Edge modes and dressing fields for the Newton-Cartan quantum Hall effect

TL;DR

This paper derives gauge-invariant edge modes for the Newton-Cartan quantum Hall effect, linking them to geometric properties and enhancing conceptual understanding within condensed matter physics.

Contribution

It provides a gauge-invariant derivation of edge modes in Newton-Cartan quantum Hall systems, connecting them to geometric aspects of the theory.

Findings

Edge modes derived in a gauge-invariant manner

Connection established between edge modes and Newton-Cartan geometry

Results align with known physics and offer deeper insight

Abstract

It is now well-known that Newton-Cartan theory is the correct geometrical setting for modelling the quantum Hall effect. In addition, in recent years edge modes for the Newton-Cartan quantum Hall effect have been derived. However, the existence of these edge modes has, as of yet, been derived using only orthodox methodologies involving the breaking of gauge-invariance; it would be preferable to derive the existence of such edge modes in a gauge-invariant manner. In this article, we employ recent work by Donnelly and Freidel in order to accomplish exactly this task. Our results agree with known physics, but afford greater conceptual insight into the existence of these edge modes: in particular, they connect them to subtle aspects of Newton-Cartan geometry and pave the way for further applications of Newton-Cartan theory in condensed matter physics.