  It has recently been established that the evolution of protoplanetary disks
is primarily driven by magnetized disk winds, requiring large-scale magnetic
flux threading the disks. The size of such disks is expected to shrink in time,
as opposed to the conventional scenario of viscous expansion. We present the
first global 2D non-ideal magnetohydrodynamic (MHD) simulations of
protoplanetary disks that are truncated in the outer radius, aiming to
understand the interaction of the disk with the interstellar environment, as
well as global evolution of the disk and magnetic flux. We find that as the
system relaxes, poloidal magnetic field threading the disk beyond the
truncation radius collapses towards the midplane, leading to rapid
reconnection. This process removes a substantial amount of magnetic flux from
the system, and forms closed poloidal magnetic flux loops encircling the outer
disk in quasi-steady-state. These magnetic flux loops can drive expansion
beyond truncation radius, corresponding to substantial mass loss through
magnetized disk outflow beyond truncation radius analogous to a combination of
viscous spreading and external photoevaporation. The magnetic flux loops
gradually shrink over time whose rates depend on level of disk magnetization
and external environments, which eventually governs the long-term disk
evolution.
