Variational Monte Carlo calculations for Bose-Hubbard model based on projected wavefunctions

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buir.advisorHetényi, Balázs
dc.contributor.authorKoç, Fulya
dc.date.accessioned2016-01-08T18:27:10Z
dc.date.available2016-01-08T18:27:10Z
dc.date.issued2014
dc.descriptionAnkara : The Department of Physics and the Graduate School of Engineering and Science of Bilkent University, 2014.en_US
dc.descriptionThesis (Master's) -- Bilkent University, 2014.en_US
dc.descriptionIncludes bibliographical references leaves 51-55.en_US
dc.description.abstractBose-Hubbard model is mainly used to describe and study the interactions between neutral atomic gases trapped in an optical lattice [1] and Josephson junction arrays [2]. It is one of the toy models to understand quantum phase transitions, i.e. a phase transition exists between the Mott insulator state and the super- fluid state. Analytical solutions are limited to obtaining the ground state energy for small systems, whereas, computational studies can be done for larger system sizes. We applied the variational Monte Carlo method to the Bose-Hubbard model based on projected wavefunctions, i.e. Baeriswyl and Gutzwiller-Baeriswyl. Even though our method can be applicable to any dimension, we only consider the one dimensional case in this thesis. We expressed observables in forms of averages over configurations to which we can apply Monte Carlo sampling techniques. Our results for both Baeriswyl and Gutzwiller projections are in qualitatively good agreement with the known calculations of the phase diagram [3,4]. Furthermore, we introduced a new method, apart from other known methods [5, 6], based on the Drude weight [7–9] to calculate the superfluid fraction, which can also be extended to observe BCS superconductivity [10].en_US
dc.description.provenanceMade available in DSpace on 2016-01-08T18:27:10Z (GMT). No. of bitstreams: 1 0006644.pdf: 426965 bytes, checksum: 51ea91f2833de18f33b1d5917b1c2558 (MD5)en
dc.description.statementofresponsibilityKoç, Fulyaen_US
dc.format.extentvii, 55 leaves, chartsen_US
dc.identifier.urihttp://hdl.handle.net/11693/15940
dc.language.isoEnglishen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectBose-Hubbard modelen_US
dc.subjectGutzwiller, Baeriswylen_US
dc.subjectVariational Monte Carloen_US
dc.subject.lccQC174.85.M64 K63 2014en_US
dc.subject.lcshMonte Carlo method.en_US
dc.subject.lcshHubbard model.en_US
dc.subject.lcshMathematical optimization.en_US
dc.titleVariational Monte Carlo calculations for Bose-Hubbard model based on projected wavefunctionsen_US
dc.typeThesisen_US
thesis.degree.disciplinePhysics
thesis.degree.grantorBilkent University
thesis.degree.levelMaster's
thesis.degree.nameMS (Master of Science)

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