Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma

TL;DR

This study uses numerical methods to analyze the transition from quantum Hall to compressible states at filling fraction 5/2, revealing a spin-polarized, incompressible ground state with phase transitions influenced by interaction strength.

Contribution

It provides new numerical evidence on the nature of the 5/2 quantum Hall state, highlighting the role of spin polarization and phase transitions to compressible states.

Findings

Ground state is spin polarized and incompressible.

Energy gap at 5/2 is about 11 times smaller than at 1/3.

Evidence of phase transitions driven by short-range interaction strength.

Abstract

Quantum Hall states at filling fraction $\nu$=5/2 are examined by numerical diagonalization. Spin-polarized and -unpolarized states of systems with $N\le 18$ electrons are studied, neglecting effects of Landau level mixing. We find that the ground state is spin polarized. It is incompressible and has a large overlap with paired states like the Pfaffian. For a given sample, the energy gap is about 11 times smaller than at $\nu$=1/3. Evidence is presented of phase transitions to compressible states, driven by the interaction strength at short distance. A reinterpretation of experiments is suggested.