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CRITICAL BEHAVIOR AND DYNAMICS OF THE SUPERFLUID-MOTT GLASS TRANSITION

Advisor:      Dr. Thomas Vojta

Date & Time:     Friday May 3, 2024 at 8:00AM

Location:     https://umsystem.zoom.us/j/97599441264   

Abstract:      This work studies the effects of disorder on the thermodynamic critical behavior and dynamical properties of the superfluid-Mott glass quantum phase transition. After a brief introduction covering relevant fundamentals, we present the dissertation in the form of four separate but related publications. In the first two publications, we calculate the thermodynamic critical exponents of the superfluid-Mott glass quantum phase transition in both two and three spatial dimensions.
The undiluted transition exhibits critical exponents that violate the Harris criterion, and thus, the critical behavior is expected to change upon introducing disorder. We confirm this behavior via Monte Carlo simulation of a diluted quantum rotor model of the transition, calculating new phase diagrams and critical behavior for the diluted systems.
In publications three and four, we investigate the dynamical properties of the collective modes near the transition boundary based on scaling arguments. These collective modes are expected to have energies that follow a power-law relationship governed by the critical exponents. In these publications, we find that in two spatial dimensions, the introduction of disorder localizes the Higgs mode, defying this expectation. In conclusion, the introduction of disorder to the superfluid-Mott insulator system has a significant effect on the thermodynamic critical behavior. In our calculations, we see that the disordered case has a new set of critical exponents that govern the power-law critical behavior of the superfluid-Mott glass transition. Despite the critical behavior of the transition being of conventional power-law type, when we consider the dynamics of the collective excitation modes, we see localization behavior that is unaccounted for in current theoretical descriptions. This shows that in disordered systems one may observe unconventional dynamical behavior in a system whose underlying thermodynamics is that of conventional power-law type.