Differences in the quasiparticle dynamics for one-band and three-band cuprate models

We study the quasiparticles of the one-band $t$-$J$ and $t$-$t'$-$t"$-$J$ models using a variational approximation that includes spin fluctuations in the vicinity of the hole. We explain why the spin fluctuations and the longer range hopping have complementary contributions to the quasiparticle dynamics, and thus why both are essential to obtain a dispersion in agreement with that measured experimentally. This is very different from the three-band Emery model in the strongly-correlated limit, where the same variational approximation shows that spin fluctuations have a minor effect on the quasiparticle dynamics. This difference proves that these one-band and three-band models describe qualitatively different quasiparticles, and therefore they they cannot both be suitable to describe the physics of underdoped cuprates.