Fractional quantum Hall state at nu=5/2 and the Moore-Read pfaffian

Area of Science:

• Quantum Hall Effect
• Condensed Matter Physics

Background:

• The fractional quantum Hall effect (FQHE) exhibits exotic states of matter.
• The state at filling factor nu=5/2 is a prime candidate for non-Abelian anyonic excitations.
• Understanding the microscopic nature of the nu=5/2 state is crucial for topological quantum computing.

Purpose of the Study:

• To investigate the relationship between the Coulomb ground state at nu=5/2 and the Moore-Read (MR) wave function.
• To determine if the MR wave function accurately describes the FQHE state at nu=5/2.
• To explore the behavior of the nu=1/2 state and its potential connection to the MR state.

Main Methods:

• Exact diagonalization techniques were employed to study systems up to 18 electrons on a spherical geometry.
• The adiabatic connection between the Coulomb ground state and the MR wave function was analyzed.
• The impact of varying Haldane pseudopotentials (v1, v3) on the energy gap and overlap was examined.

Main Results:

• An adiabatic connection was established between the spin-polarized Coulomb ground state and the MR wave function for nu=5/2 systems.
• A large energy gap protects the ground state across all studied system sizes.
• The positions and extent of energy gap and overlap hills in the (v1, v3) plane coincide, supporting the MR state's validity.
• An adiabatic connection was not found for the nu=1/2 state under typical conditions.

Conclusions:

• The Moore-Read wave function effectively captures the physics of the Coulomb ground state at nu=5/2.
• The nu=1/2 state does not exhibit a robust adiabatic connection to the MR state, suggesting it is unlikely in the thermodynamic limit.
• The findings support the potential of the nu=5/2 state for realizing topological quantum computing.