Theories of Experimentally Observed Excitation Spectra of Square Lattice Antiferromagnets

The first part of this thesis presents the theoretical study of an anomaly of unknown origin in the excitation spectrum of the Quantumspin-1/2 Heisenberg Square lattice Anti-Ferromagnet. The anomaly manifests itself in Inelastic Neutron Scattering data for short wavelength/high energy excitations. Instead of the expected sharp semi-classical harmonic modes, a broad continuum emerges suggesting the possibility of fractionalized excitations. A theoretical framework based on the Gutzwiller projection is developed and allows to link the observed continuum to unbound fractional quasiparticle pairs while the sharp harmonic excitations may be described by bound ones. The second part of this thesis presents the detailed theoretical modeling of the spin-wave dispersion relation measured in insulating cuprate materials. Starting from the one-band Hubbard model with extended hopping amplitudes, an effective low-energy theory is derived allowing to describe on the same footing different insulating cuprate magnetic excitation spectra. The effective theory is fitted against experimental data and microscopic model parameters are extracted. The high level of details included in our effective theory allows a consistent characterization of the studied materials as measured by various magnetic or electronic experimental techniques.