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Edge Modes and Dressing Fields for the Newton-Cartan Quantum Hall Effect.
William J Wolf1, James Read1, Nicholas J Teh2
1Faculty of Philosophy, University of Oxford, Radcliffe Humanities, Woodstock Road, Oxford, OX2 6GG UK.
Foundations of Physics
|December 1, 2022
Summary
This study presents a gauge-invariant derivation of edge modes in the Newton-Cartan quantum Hall effect. The findings connect these modes to Newton-Cartan geometry, offering new insights and applications in condensed matter physics.
Area of Science:
- Theoretical Physics
- Condensed Matter Physics
- Quantum Field Theory
Background:
- Newton-Cartan theory provides the geometric framework for the quantum Hall effect.
- Previous derivations of edge modes in this context relied on gauge-invariance breaking methods.
Purpose of the Study:
- To derive the existence of edge modes for the Newton-Cartan quantum Hall effect in a gauge-invariant manner.
- To provide greater conceptual insight into these edge modes and their connection to geometry.
Main Methods:
- Utilized recent work by Donnelly and Freidel.
- Employed gauge-invariant methodologies.
Main Results:
- Successfully derived edge modes for the Newton-Cartan quantum Hall effect without breaking gauge-invariance.
- Established a connection between these edge modes and subtle aspects of Newton-Cartan geometry.
Conclusions:
- The gauge-invariant derivation offers a more rigorous understanding of edge modes.
- The results pave the way for novel applications of Newton-Cartan theory in condensed matter physics.
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