  Seconds-long numerical-relativity simulations for black hole-neutron star
mergers are performed for the first time to obtain a self-consistent picture of
the merger and post-merger evolution processes. To investigate the case that
tidal disruption takes place, we choose the initial mass of the black hole to
be $5.4M_\odot$ or $8.1M_\odot$ with the dimensionless spin of 0.75. The
neutron-star mass is fixed to be $1.35M_\odot$. We find that after the tidal
disruption, dynamical mass ejection takes place spending $\lesssim 10$ ms
together with the formation of a massive accretion disk. Subsequently, the
magnetic field in the disk is amplified by the magnetic winding and
magnetorotational instability, establishing a turbulent state and inducing the
angular momentum transport. The post-merger mass ejection by the
magnetically-induced viscous effect sets in at $\sim 300$-500\,ms after the
tidal disruption, at which the neutrino luminosity drops below $\sim
10^{51.5}\,{\rm erg/s}$, and continues for several hundreds ms. A magnetosphere
near the rotational axis of the black hole is developed after the matter and
magnetic flux fall into the black hole from the accretion disk, and
high-intensity Poynting flux generation sets in at a few hundreds ms after the
tidal disruption. The intensity of the Poynting flux becomes low after the
significant post-merger mass ejection, because the opening angle of the
magnetosphere increases. The lifetime for the stage with the strong Poynting
flux is $1$-2 s, which agrees with the typical duration of short-hard gamma-ray
bursts.
