Possible restoration of particle-hole symmetry in the 5/2 Quantized Hall State at small magnetic field

TL;DR

This paper investigates the potential restoration of particle-hole symmetry in the 5/2 quantum Hall state at low magnetic fields, suggesting a phase transition that aligns with experimental thermal conductance observations.

Contribution

It extends the effective Hamiltonian to third-order in Landau level mixing and shows that Pfaffian and AntiPfaffian states become nearly degenerate at small magnetic fields.

Findings

Overlap difference between Pfaffian and AntiPfaffian diminishes at small magnetic field.

Finite-size spectrum indicates a quantum phase transition with level crossings.

Energy gap reduces significantly near the transition point.

Abstract

Motivated by the experimental observation of a quantized 5/2 thermal conductance at filling $\nu=5/2$, a result incompatible with both the Pfaffian and the Antipfaffian states, we have pushed the expansion of the effective Hamiltonian of the $5/2$ quantized Hall state to third-order in the parameter $\kappa=E_c/\hbar \omega_c \propto 1/\sqrt{B}$ controlling the Landau level mixing , where $E_c$ is the Coulomb energy and $\omega_c$ the cyclotron frequency. Exact diagonalizations of this effective Hamiltonian show that the difference in overlap with the Pfaffian and the AntiPfaffian induced at second-order is reduced by third-order corrections and disappears around $\kappa=0.4$, suggesting that these states are much closer in energy at smaller magnetic field than previously anticipated. Furthermore, we show that in this range of $\kappa$ the finite-size spectrum is typical of a quantum phase transition, with a strong reduction of the energy gap and with level crossings between excited states. These results point to the possibility of a quantum phase transition at smaller magnetic field into a phase with an emergent particle-hole symmetry that would explain the measured $5/2$ thermal conductance of the $5/2$ quantized Hall state.