Browsing by Subject "Variational Monte Carlo"
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Item Open Access Fractional quantum Hall states in the vicinity of Mott plateaus(The American Physical Society, 2010) UmucalIlar, R. O.; Mueller, E. J.We perform variational Monte Carlo calculations to show that bosons in a rotating optical lattice will form analogs of fractional quantum Hall states when the tunneling is sufficiently weak compared to the interactions, and the deviation of density from an integer is commensurate with the effective magnetic field. We compare the energies of superfluid and correlated states to one another and to the energies found in full configuration-interaction calculations on small systems. We look at overlaps between our variational states and the exact ground state, characterizing the ways in which fractional quantum Hall effect correlations manifest themselves near the Mott insulating state. We explore the experimental signatures of these states.Item Open Access Variational Monte Carlo calculations for Bose-Hubbard model based on projected wavefunctions(2014) Koç, FulyaBose-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].Item Open Access Variational Monte Carlo study of two dimensional charged bosons(2014-09) Karakuzu, SeherWe studied the ground state properties of 2D charged Bosons interacting via Coulomb potential using the Variational Monte Carlo method. We start with the paper of McMillan [1] in which there are 3D Bosons interacting via Lennard-Jones potential. We calculate ground state energy and pair distribution function of the system and our results are compared with the original work. We also reproduce the paper of Liu et al. [2] and study the 2D Bosons interacting with the same potential. Our results are compared with the original work. In order to evaluate long-range potentials in periodic systems we introduce Ewald summation method for 2D system and Natoli-Ceperley method which evaluates potentials optimally. We compare our Natoli-Ceperley results with the Holzmann et al. [3]. We also investigate 2D charged Boson system interacting via Coulomb potential using the RPA pseudo potential. Our results are compared with de Palo et al. [4]. We try to optimize the wave function further introducing a Kinetic Energy projection to the original RPA wave function. We show that it is very difficult to optimize it further since it is a very good wave function.