| This dissertation covers some aspects of quantum magnetism in strongly interacting two and three dimensional insulators. In the first chapter we study the various phases of the Rokhsar-Kivelson quantum dimer model. We use a recently developed Hamiltonian formulation of quantum field theory to investigate the frustrated lattice gauge theory version of the quantum dimer model. A variational approach is used to obtain insights into the strongly interacting non-perturbative aspects of the ground state. The valence bond crystal is obtained in the v << t limit. We demonstrate that the physics of the Rokhsar-Kivelson point can be obtained self-consistently at a special point in the phase space. We show that a dynamical cancellation of compact gauge excitations is responsible for soft massless photons.; The second chapter deals with the quantum Heisenberg Hamiltonian on the geometrically frustrated pyrochlore lattice. We use a Gutzwiller projected SU(N) mean field approach to study various saddle point states. The most promising state is a spin liquid that breaks parity and time-reversal at the microscopic level. Nonetheless, the low energy theory does not break parity or time-reversal. In this respect, it is similar to anti-ferromagnetism. The state has massless spinons and gauge fluctuations. We show that this property persists for a class of perturbations. |
