Theoretical developments in low-dimensional magnetic systems

In this thesis, we investigate low-dimensional magnetic systems from the theoretical points of view. To address situations with several and distinct magnetic interactions, we develop different frameworks, including a magnon self-energy approach, a spin dynamical exchange-correlation (xc) field formalism and a scheme combining Matrix Product States method and exact diagonalization/nonequilibrium Green's function methods (MPS + ED/NEGF). By means of effective models, we study topics including magnetic frustration, homogeneous spin chain, magnetic skyrmions, and magnetic impurities.

The thesis is based on four papers: In Paper I, we apply the magnon self-energy approach to study the ground-state properties of two-dimensional Heisenberg models with competing exchange couplings. In Papers II and IV, the dynamical xc field formalism is used to calculate the Green's function. In Paper II, we propose a spin xc field formalism to calculate dynamical spin structure factor of the one-dimensional antiferromagnetic Heisenberg model at zero-temperature. In Paper IV, we investigate the Kondo spectral function by extending the xc field formalism to finite temperatures, and apply the formalism to the single-impurity Anderson model. In Paper III, we propose a MPS + ED/NEGF scheme to calculate the ground-state and dynamical properties of quantum magnetic skyrmions with itinerant electrons explicitly included.