Wave function and size of spin-polarons in the t-J model

Here we present a more detailed picture of some spatial properties of the spin-polaron - quasiparticle formed after injecting a hole into a planar quantum antiferromagnet. The explicit form of the quasiparticle wave function allows us accurately to investigate the spatial extent of the polaron. In the Ising limit of the model we find for the RMS radius of the distribution of spin-deviations around the moving hole is R = 1.06(t/J)(0.157). The form and the size of the polaron in the usual t-J model (Heisenberg limit), is on the other hand, anisotropic, larger and does not obey such a simple scaling. Finally we discuss the renormalization of spin-polarons by phonons in the framework of a Holstein t-J model.