Quantum Monte Carlo studies of phase transitions

Phase transitions have been an active area of research in statistical mechanics for almost a century and have recently been integrated into quantum mechanics. Many phenomena such as superconductivity and unconventional magnetism are understood to arise from exotic quantum phases and at points describing quantum phase transitions. A detailed understanding of these phase transitions requires numerical simulations of models which benchmark realistic models against theoretical frameworks. The topic of this thesis is the implementation of Quantum Monte Carlo simulation, which is a powerful technique to understand quantum condensed matter, in interesting models to illustrate novel phenomena in magnetic systems. The novel features of condensed matter systems described in this thesis consist of emergent symmetries at critical points, interesting dynamical features of such systems and the drastic effects of defects in spin systems used in the field of adiabatic quantum computing. Emergent symmetries are shown by condensed matter systems especially at critical points and are features which cannot be shown by individual or a small number of spins. Examples of this in one and two dimensions are presented in an early chapter of this thesis. In addition to this, spin systems can show excitations which have an interesting spatial structure as a consequence of restricted dynamics which only allow the excitations to spread in a particular region. This is presented in the context of a simple model in the following chapter along with numerical support. The following chapter contains a description of adiabatic quantum computing along with a particular model which we study. The phase transition and the effects on the performance of adiabatic quantum computing are studied in this context