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.
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