dc.rights.license | CC-BY-NC-ND | |
dc.contributor.advisor | Fritz, L. | |
dc.contributor.author | Breebaart, Rik | |
dc.date.accessioned | 2023-02-21T01:00:49Z | |
dc.date.available | 2023-02-21T01:00:49Z | |
dc.date.issued | 2023 | |
dc.identifier.uri | https://studenttheses.uu.nl/handle/20.500.12932/43559 | |
dc.description.abstract | We give a discussion on the Hybrid Monte Carlo simulations of the tight binding model with Coulomb
interactions, for the electronic properties of Graphene. The aim of our simulations is to determine
the phase transition in which Graphene goes from a semimetal to an insulator through spontaneous
breaking of sublattice symmetry. This is done non-perturbatively using lattice field theory techniques,
working in the path-integral formalism with discrete euclidean time. We explain the method by
[Brower, Rebbi and Schaich, arXiv:1101.5131v1, 26 Jan 2011] through which the theory of Graphene
can be written in a form independent of a sign problem. An implementation of this method has been
made in Julia, and can be found in [https://github.com/Rik-Breebaart/GrapheneHMC.git]. Our
measurements show no clear phase-transition in the order parameters for this sublattice symmetry
breaking. However, the system sizes on which the simulation have been performed where to small to
make conclusive prediction on the presence and critical value of the phase-transition. | |
dc.description.sponsorship | Utrecht University | |
dc.language.iso | EN | |
dc.subject | The thesis discusses a lattice field theory of graphene with the aim of finding a phase transition dependent on the interaction strength. It describes the methods used to perform such calculations, including the Hybrid Monte Carlo method of integration, the necessary transformations needed to remove the sign problem and the specific observables to view the transition. | |
dc.title | Hybrid Monte Carlo Simulations of Graphene | |
dc.type.content | Master Thesis | |
dc.rights.accessrights | Open Access | |
dc.subject.keywords | Monte Carlo; Graphene; Lattice Field Theory; Hybrid Monte Carlo; | |
dc.subject.courseuu | Theoretical Physics | |
dc.thesis.id | 14115 | |