Interacting like charges in Landau levels: Planar geometry, symmetries, and effective quasiparticles

TL;DR

This paper develops a theoretical framework for two interacting particles with unequal charges in a magnetic field, constructing a basis compatible with symmetries and deriving analytical eigenenergies for Landau levels.

Contribution

It introduces a canonical transformation linking effective quasiparticles to SU(2) algebra, enabling analytical calculation of eigenenergies in Landau levels.

Findings

Analytical eigenenergies for Landau levels derived

Complete basis compatible with symmetries constructed

Connection established between transformations and SU(2) algebra

Abstract

We consider a system of two interacting particles with like but unequal charges in a magnetic field in the planar geometry. We construct a complete basis of states compatible with both the axial symmetry and magnetic translations. The basis is obtained using a canonical transformation that generates effective quasiparticles with modified interactions. We establish a connection of this transformation with the SU(2) algebra and make use of the SU(2) Baker-Campbell-Hausdorff formulas for evaluating the interaction matrix elements. We calculate analytically the eigenenergies of the problem (Haldane pseudopotentials) in the first few Landau levels for a relatively wide class of interaction potentials.