Physics of Resonating Valence Bond Spin Liquids

This thesis will investigate various aspects of the physics of resonating valence bond spin liquids. After giving an introduction to the world that lies beyond Landau\u27s priciple of symmetry breaking, e.g. giving an overview of exotic magnetic phases and how they can be described and: possibly) found, we will study a spin-rotationally invariant model system with a known parent Hamiltonian, and argue its ground state to lie within a highly sought after exotic phase, namely the Z$_{2}$ quantum spin liquid phase. A newly developed numerical procedure --Pfaffian Monte Carlo-- will be introduced to amass evidence that our model Hamiltonian indeed exhibits a Z$_{2}$ quantum spin liquid phase. Subsequently, we will prove a useful mathematical property of the resonating valence bond states: these states are shown to be linearly independent. Various lattices are investigated concerning this property, and its applications and usefullness are discussed. Eventually, we present a simplified model system describing the interplay of the well known Heisenberg interaction and the Dzyaloshinskii-Moriya: DM) interaction term acting on a sawtooth chain. The effect of the interplay between the two interaction couplings on the phase diagram is investigated. To do so, we employ modern techniques such as the density matrix renormalization group: DMRG) scheme. We find that for weak DM interaction the system exhibits valence bond order. However, a strong enough DM coupling destroys this order