Exact Symmetries of Electron Interactions in the Lowest Landau Level

TL;DR

This paper demonstrates that the Hamiltonian describing interacting electrons in the lowest Landau level exhibits a universal local area-preserving symmetry, regardless of specific interaction potentials, revealing fundamental invariance properties.

Contribution

It establishes the universality of local area-preserving symmetry in the four-fermion Hamiltonian for electrons in the lowest Landau level across various interaction potentials.

Findings

Hamiltonian is invariant under local area-preserving transformations

Symmetry is universal for a class of interaction potentials

Provides insight into fundamental invariance in quantum Hall systems

Abstract

Considering the system of interacting electrons in the lowest Landau level we show that the corresponding four-fermion Hamiltonian is invariant with respect to the local area-preserving transformations. Testing a certain class of interaction potentials, we find that this symmetry is universal with respect to a concrete type of potentials.