Figure 1: (Top) The string of defects (emphasized by blue halos) that are generated by hole motion in an antiferromagnetic background can be “healed” by quantum fluctuations. (Bottom) A similar string of defects (blue halos) is generated by zigzag hole motion in an alternating-orbital-order background (the green and purple lobes represent orbitals with $xz$ and $yz$ symmetry, respectively). These cannot be healed by quantum fluctuations and instead the hole has to do it by retracing its steps. Overall hole motion is enabled by three-site processes (red halos), consisting of directional tunneling through a doubly occupied site without generating a defect.