Hole propagation in the orbital compass models
  We explore the propagation of a single hole in the generalized quantum compass model which interpolates between fully isotropic antiferromagnetic (AF) phase in the Ising model and nematic order of decoupled AF chains for frustrated compass interactions. We observe coherent hole motion due to either interorbital hopping or due to the three-site effective hopping, while quantum spin fluctuations in the ordered background do not play any role. 
Wojciech Brzezicki. Maria Daghofer and Andrzej M. Ole\'s
cond-mat.str-el quant-ph