# Direct-exchange duality of the Coulomb interaction and collective excitations in graphene in a magnetic field

## TL;DR

This paper introduces a novel algorithm leveraging the direct-exchange duality of Coulomb interactions to efficiently analyze collective excitations in graphene and similar 2D electron systems under magnetic fields.

## Contribution

It develops a new algorithm based on Coulomb interaction duality, enabling improved analysis of collective excitations in 2D electron systems in magnetic fields.

## Key findings

- Demonstrates the algorithm's utility on Landau-level excitations in graphene.
- Shows the duality simplifies the treatment of Coulomb interactions.
- Provides insights into collective phenomena in quantum Hall systems.

## Abstract

In a magnetic field two-dimensional (2d) electron systems host, with quenched kinetic energy, a variety of many-body correlation phenomena, such as interaction-driven new states and associated collective excitations over them. In a magnetic field the two-body operators pertinent to the 2d Coulomb interaction obey a crossing relation, with which the Coulomb interaction is also cast into the form of manifest exchange interaction. It is shown that active use of this direct/exchange duality of the interaction allows one to develop, within the framework of the single-mode approximation, a new efficient algorithm for handling a wide class of collective excitations. The utility of our algorithm is demonstrated by studying some examples of inter- and intra-Landau-level collective excitations in graphene and in conventional electron systems.