# Landau-level-mixing and the ground state of the 5/2 quantum Hall effect

## TL;DR

This paper investigates the impact of Landau-level mixing on the ground state of the 5/2 fractional quantum Hall effect, finding that it favors the anti-Pfaffian state through a perturbative approach.

## Contribution

It introduces a perturbation theory method that unbiasedly determines the ground state, highlighting the importance of a previously omitted term in the effective Hamiltonian.

## Key findings

- Landau-level mixing favors the anti-Pfaffian state.
- A critical term in the effective Hamiltonian reverts the ground state to anti-Pfaffian.
- The method provides an unbiased approach to determine the ground state.

## Abstract

Inter-Landau-level transitions break particle hole symmetry and will choose either the Pfaffian or the anti-Pfaffian state as the absolute ground state at 5/2 filling of the fractional quantum Hall effect. An approach based on truncating the Hilbert space has favored the anti-Pfaffian. A second approach based on an effective Hamiltonian produced the Pfaffian. In this letter perturbation theory is applied to finite sizes without bias to any specific pseudo-potential component. This method also singles out the anti-Pfaffian. A critical piece of the effective Hamiltonian, which was absent in previous studies, reverts the ground state at 5/2 to the anti-Pfaffian.