The fate of spin-charge separation in the presence of long-range antiferromagnetism

We present a numerical study of competing orders in the 1D t-J model with long range RKKY-like staggered spin interactions. By circumventing the constraints imposed by Mermin-Wagner's theorem, this Hamiltonian can realize long-range Néel order at and near half-filling. Upon doping, interactions induce a confining potential that binds holons and spinons forming full fledged polaronic quasi-particles. We determine the full phase diagram as a function of the exchange and density using the density matrix renormalization group (DMRG) method. We show that pairing is disfavored and the AFM insulator and polaronic metal phase are separated by a range of densities with phase segregation, while spin-charge separation re-emerges at low densities. In addition, we calculate the photoemission spectrum of the model, showing the emergence of a coherent polaronic band splitting away from the holon-spinon continuum with a regime realizing hole pockets.