Hole Properties In and Out of Magnetization Plateaus in 2-d Antiferromagnet

We study the signatures of magnetization plateaus and the presence or absence of Goldstone modes in terms of their effects on the physics of holes in hole-doped two-dimensional antiferromagnet defined on square lattice. Holes with quadratic dispersion around Fermi point existing at infinitesimally small doping and linear dispersion around nearly circular Fermi surface at finite but low doping are investigated. They are coupled to an effective gauge field, generated by the spin sector, which subsequently mediates interaction between the holes. We find that out-of-plateaus case leads to algebraically decaying long-range interaction between fermionic holes with both Coulombic and dipolar forms, whereas in-plateaus case leads to short-range (local) interaction. We show that the spectral peak is significantly broadened in the out-of-plateaus case, while the spectral weight is still sharply-peaked in the in-plateau case. This conclusion holds in both infinitesimally small doping limit and in the more realistic finite doping case. We also extend the result obtained for 1-D system where finite hole doping gives rise to a shift in the magnetization value of the plateaus. Reference: arXiv:1411.1713