Critical properties of effective gauge theories for novel quantum fluids

Abstract

Critical properties of U(1) symmetric gauge theories are studied in 2+1 dimensions, analytically through duality transformations and numerically through Monte Carlo simulations. Physical applications range from quantum phase transitions in two dimensional insulating materials to super uid and superconducting properties of light atoms such as hydrogen under extreme pressure. A novel finite size scaling method, utilizing the third moment M3 of the action, is developed. Finite size scaling analysis of M3 yields the ratio (1 + α)=/ υ and 1= /v separately, so that critical exponents α and v can be obtained independently without invoking hyperscaling. This thesis contains eight research papers and an introductory part covering some basic concepts and techniques.