Spin polarization of the $\nu =5\mathrm{/}2$ quantum Hall state

We report on results of numerical studies of the spin polarization of the half filled second Landau level, which corresponds to the fractional quantum Hall state at filling factor $\nu =5\mathrm{/}2$. Our studies are performed using both exact diagonalization and Density Matrix Renormalization Group (DMRG) on the sphere. We find that for the Coulomb interaction the exact finite-system ground state is fully polarized, for shifts corresponding to both the Moore-Read Pfaffian state and its particle-hole conjugate (anti-Pfaffian). This result is found to be robust against small variations of the interaction. The low-energy excitation spectrum is consistent with spin-wave excitations of a fully-magnetized ferromagnet.