We study the field dependence of the antiferromagnetic spin-1/2 Heisenberg model on the square lattice by means of exact diagonalizations. In a first part, we calculate the spin-wave velocity, the spin-stiffness, and the magnetic susceptibility and t
hus determine the microscopic parameters of the low-energy long-wavelength description. In a second part, we present a comprehensive study of dynamical spin correlation functions for magnetic fields ranging from zero up to saturation. We find that at low fields, magnons are well defined in the whole Brillouin zone, but the dispersion is substantially modified by quantum fluctuations compared to the classical spectrum. At higher fields, decay channels open and magnons become unstable with respect to multi-magnon scattering. Our results directly apply to inelastic neutron scattering experiments.
We explore the pairing properties of the one-dimensional attractive Hubbard model in the presence of finite spin polarization. The correlation exponents for the most important fluctuations are determined as a function of the density and the polarizat
ion. We find that in a system with spin population imbalance, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-type pairing at wavevector Q=|k_{F,uparrow}-k_{F,downarrow}| is always dominant and there is no Chandrasekhar-Clogston limit. We then investigate the case of weakly coupled 1D systems and determine the region of stability of the 1D FFLO phase. This picture is corroborated by density-matrix-renormalization-group (DMRG) simulations of the spatial noise correlations in uniform and trapped systems, unambiguously revealing the presence of fermion pairs with nonzero momentum Q. This opens up an interesting possibility for experimental studies of FFLO states.
