Physics (Internal)

Quantum Monte Carlo Studies of Phase Transitions

This event is part of the PhD Final Oral Exams.

Dissertation Committee: Anders Sandvik, Claudio Chamon, David Campbell, Alex Sushkov, Emanuel Katz

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, for interesting models to illustrate novel phenomena in magnetic systems. The novel features of condensed matter systems which will be described in this talk 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 will be presented in this talk. 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 will be presented in the context of a simple model here, along with numerical support. This is followed by 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.