Supersymmetric quantum-Hall effect on a fuzzy supersphere

Area of Science:

• Condensed Matter Physics
• High Energy Physics
• Quantum Field Theory

Background:

• Quantum-Hall liquids exhibit exotic topological properties.
• Supersymmetry offers a powerful framework for unifying particles and forces.
• The interplay between these fields remains an active area of research.

Purpose of the Study:

• To construct supersymmetric quantum-Hall liquids.
• To generalize the Laughlin wave function within a supersymmetric framework.
• To explore the nature of topological excitations in these systems.

Main Methods:

• Construction of quantum-Hall liquids on a supersphere in a supermonopole background.
• Derivation of a supersymmetric generalization of the Laughlin wave function.
• Analysis of excited topological objects, including fractionally charged deficits.

Main Results:

• A novel supersymmetric generalization of the Laughlin wave function was derived.
• This wave function describes the ground state of a hard-core OSp(1/2) invariant Hamiltonian.
• Excited topological objects, characterized by fractional charges generated by super Hall currents, were identified.

Conclusions:

• The study successfully constructed supersymmetric quantum-Hall liquids.
• New insights into the topological properties and excitations of these systems were gained.
• Connections between standard quantum-Hall systems and their supersymmetric extensions were elucidated.