Quantum Treatment of the Anderson-Hasegawa Model -- Effects of   Superexchange and Polarons
  We revisit the Anderson-Hasegawa double-exchange model and critically examine its exact solution when the core spins are treated quantum mechanically.We show that the quantum effects, in the presence of an additional superexchange interaction between the core spins, yield a term, the significance of which has been hitherto ignored. The quantum considerations further lead to new results when polaronic effects, believed to be ubiquitous in manganites due to electron-phonon coupling, are included. The consequence of these results for the magnetic phase diagrams and the thermal heat capacity is also carefully analysed. 
Manidipa Mitra, P. A. Sreeram and Sushanta Dattagupta