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dc.contributor.authorLiu, Cheng-Weien_US
dc.date.accessioned2016-04-06T16:00:41Z
dc.date.available2016-04-06T16:00:41Z
dc.date.issued2015
dc.identifier.urihttps://hdl.handle.net/2144/15436
dc.description.abstractPhase transitions and their associated critical phenomena are of fundamental importance and play a crucial role in the development of statistical physics for both classical and quantum systems. Phase transitions embody diverse aspects of physics and also have numerous applications outside physics, e.g., in chemistry, biology, and combinatorial optimization problems in computer science. Many problems can be reduced to a system consisting of a large number of interacting agents, which under some circumstances (e.g., changes of external parameters) exhibit collective behavior; this type of scenario also underlies phase transitions. The theoretical understanding of equilibrium phase transitions was put on a solid footing with the establishment of the renormalization group. In contrast, non-equilibrium phase transition are relatively less understood and currently a very active research topic. One important milestone here is the Kibble-Zurek (KZ) mechanism, which provides a useful framework for describing a system with a transition point approached through a non-equilibrium quench process. I developed two efficient Monte Carlo techniques for studying phase transitions, one is for classical phase transition and the other is for quantum phase transitions, both are under the framework of KZ scaling. For classical phase transition, I develop a non-equilibrium quench (NEQ) simulation that can completely avoid the critical slowing down problem. For quantum phase transitions, I develop a new algorithm, named quasi-adiabatic quantum Monte Carlo (QAQMC) algorithm for studying quantum quenches. I demonstrate the utility of QAQMC quantum Ising model and obtain high-precision results at the transition point, in particular showing generalized dynamic scaling in the quantum system. To further extend the methods, I study more complex systems such as spin-glasses and random graphs. The techniques allow us to investigate the problems efficiently. From the classical perspective, using the NEQ approach I verify the universality class of the 3D Ising spin-glasses. I also investigate the random 3-regular graphs in terms of both classical and quantum phase transitions. I demonstrate that under this simulation scheme, one can extract information associated with the classical and quantum spin-glass transitions without any knowledge prior to the simulation.en_US
dc.language.isoen_US
dc.rightsAttribution 4.0 Internationalen_US
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectPhysicsen_US
dc.subjectQAQMCen_US
dc.subjectNon-equilibrium quenchen_US
dc.subjectQuantum annealingen_US
dc.subjectQuantum Monte Carloen_US
dc.subjectRegular graphsen_US
dc.subjectSpin-glassen_US
dc.titleComputational studies of thermal and quantum phase transitions approached through non-equilibrium quenchingen_US
dc.typeThesis/Dissertationen_US
dc.date.updated2016-03-12T07:13:16Z
etd.degree.nameDoctor of Philosophyen_US
etd.degree.leveldoctoralen_US
etd.degree.disciplinePhysicsen_US
etd.degree.grantorBoston Universityen_US


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Attribution 4.0 International
Except where otherwise noted, this item's license is described as Attribution 4.0 International