Particle-Hole Symmetry Breaking and the 5/2 Fractional Quantum Hall Effect

TL;DR

This study investigates the 5/2 fractional quantum Hall effect, revealing a sharp transition between Pfaffian and anti-Pfaffian states influenced by particle-hole symmetry breaking and identifying phase transitions to compressible states.

Contribution

It demonstrates how three-body interactions induce a transition between Pfaffian and anti-Pfaffian states, providing a detailed phase diagram of the system.

Findings

Sharp transition between Pfaffian and anti-Pfaffian states at Coulomb point

Particle-hole symmetry breaking influences ground state selection

Transitions to compressible phases occur with pseudopotential changes

Abstract

We report on the study of the fractional quantum Hall effect at the filling factor 5/2 using exact diagonalization method with torus geometry. The particle-hole symmetry breaking effect is considered using an additional three-body interaction. Both Pfaffian and anti-Pfaffian states can be the ground state depending on the sign of the three-body interaction. The results of the low-energy spectrum, the wave function overlap, and the particle-hole parity evolution, have shown the clear evidence of a direct sharp transition (possibly first-order) from the Pfaffian to the anti-Pfaffian state at the Coulomb point. A quantum phase diagram is established, where one finds further transitions from the Pfaffian or anti-Pfaffian state to the nearby compressible phases induced by a change of the pseudopotential.