Off-campus UMass Amherst users: To download campus access dissertations, please use the following link to log into our proxy server with your UMass Amherst user name and password.
Non-UMass Amherst users: Please talk to your librarian about requesting this dissertation through interlibrary loan.
Dissertations that have an embargo placed on them will not be available to anyone until the embargo expires.
Author ORCID Identifier
N/A
AccessType
Open Access Dissertation
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Physics
Year Degree Awarded
2018
Month Degree Awarded
September
First Advisor
Nikolay Prokof'ev
Second Advisor
Boris Svistunov
Subject Categories
Atomic, Molecular and Optical Physics | Condensed Matter Physics | Quantum Physics
Abstract
In this dissertation, we study the superfluid-insulator quantum phase transition in disordered boson systems. Recently, there has been considerable controversy over the validity of the scaling relations of the superfluid--Bose-glass quantum phase transition in three dimensions. Results from experimental and numerical studies on disordered quantum magnets contradict the scaling relations and the associated conventional scaling hypothesis for the singular part of the free energy. We determine various critical exponents of the superfluid--Bose-glass quantum phase transition in three-dimensional disordered Bose-Hubbard model through extensive Monte Carlo simulations. Our numerical study shows the previous studies on disordered quantum magnets were performed outside the quantum critical region, and our results for the critical exponents are in perfect agreement with previous theoretical predictions.
We next move to study theoretically and numerically the superfluid-insulator quantum phase transition in one-dimensional disordered boson systems. While the superfluid-insulator transition in the weak disorder limit is well understood through the perturbative renormalization group study by Giamarchi and Schulz, transitions in the strong disorder regime are beyond the reach of this method. This problem was recently attacked by Altman et al. with the real space renormalization group method. They reached the conclusion that the superfluid-insulator transition in the strong disorder regime can be explained by the Coulomb blockade physics of weak links. However, their method is actually uncontrolled. Taking account of the crucial role of the hydrodynamic renormalization of weak links, finally, Pollet et al. put forward an asymptotically exact renormalization group theory of the superfluid-insulator transition. Based on this theory, we are able to provide an accurate description of the interplay between the well-known Giamarchi-Schulz criticality and the new weak-link criticality. A significant part of the ground-state phase diagram of one-dimensional disordered Bose-Hubbard model at unit filling is also determined numerically. In particular, we established the position of the multicritical point beyond which the new weak-link criticality takes over of the Giamarchi–Schulz criticality.
DOI
https://doi.org/10.7275/12500150
Recommended Citation
Yao, Zhiyuan, "QUANTUM PHASE TRANSITIONS IN DISORDERED BOSON SYSTEMS" (2018). Doctoral Dissertations. 1396.
https://doi.org/10.7275/12500150
https://scholarworks.umass.edu/dissertations_2/1396
Included in
Atomic, Molecular and Optical Physics Commons, Condensed Matter Physics Commons, Quantum Physics Commons