Degeneracy of Multi-Component Quantum Hall States Satisfying Periodic Boundary Conditions

TL;DR

This paper investigates the degeneracy properties of multi-component quantum Hall states under periodic boundary conditions, revealing additional degeneracies beyond known center of mass translation symmetries, with implications for numerical analysis.

Contribution

It extends the understanding of degeneracies in quantum Hall states to multi-component systems, identifying new degeneracies relevant for computational studies.

Findings

Multi-component systems exhibit extra degeneracies.

Degeneracies relate to symmetries beyond center of mass translations.

Implications for numerical simulations of quantum Hall states.

Abstract

In systems subject to periodic boundary conditions, Haldane has shown that states at arbitrary filling fraction possess a degeneracy with respect to center of mass translations. An analysis is carried out for multi-component electron systems and extra degeneracies are shown to exist. Their application to numerical studies is discussed.