Itinerant quasiparticle theory of the Mott insulator

     Linear spin wave theory of the Heisenberg model is foundational to the understanding of insulating antiferromagnetism, yet the canonical Holstein-Primakoff boson remains heretofore disconnected from itinerant electron dynamics.  By subtracting correlated hopping from the Hubbard-Heisenberg model, this work shows an itinerant, charged dynamic that precisely encompasses the chargeless Heisenberg model.  Specifically, time-dependent Hartree-Fock theory exactly reconciles with the H-P boson, yielding a spin wave dispersing with J_ij, but strictly independent of t_ij and U.  The equivalence holds when the Mott insulator is stable when Hubbard U dominates intra-sublattice bandwidth, U > W[t'_ij].

     At finite doping, the spin wave is Landau damped by the lower Hubbard band, and a zero sound mode disperses, both contingent on the presence and strength of inter-sublattice hopping. Beyond the usual spin and spacetime symmetries, the dynamic is doublon conserving and has SU(2) charge symmetry. Detuning correlated hopping renders potent p-h asymmetry distinct from flipping the sign of t' in the t'-t'-J model.

     Severe instabilities present when U is small while retaining strongly correlated hopping, pointing to limitations of the quasiparticle picture and expectations of quantum order. This work aims to motivate study of the symmetric and detuned dynamics with general (non-quasiparticle) analytical and numerical methods, in the context of cuprate phenomenology.