Browsing by Subject "Bose-Hubbard model"

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Open Access
Neural-network quantum states for a two-leg bose-hubbard ladder under a synthetic magnetic field
(2023-07) Çeven, Kadir
This thesis explores novel quantum phases in a two-leg Bose-Hubbard ladder, achieved using neural-network quantum states. The remarkable potential of quantum gas systems for analog quantum simulation of strongly correlated quantum matter is well-known; however, it is equally evident that new theoretical bases are urgently required to comprehend their intricacies fully. While simple one dimensional models have served as valuable test cases, ladder models naturally emerge as the next step, enabling studying higher dimensional effects, including gauge fields. Utilizing the paper [Çeven et al., Phys. Rev. A 106, 063320 (2022)], this thesis investigates the application of neural-network quantum states to a two leg Bose-Hubbard ladder in the presence of strong synthetic magnetic fields. This paper showcased the reliability of variational neural networks, such as restricted Boltzmann machines and feedforward neural networks, in accurately predicting the phase diagram exhibiting superfluid-Mott insulator phase transition under strong interaction. Moreover, the neural networks successfully identified other intriguing many-body phases in the weakly interacting regime. These exciting findings firmly designate a two-leg Bose-Hubbard ladder with magnetic flux as an ideal testbed for advancing the field of neural-network quantum states. By expanding these previous results, this thesis contains various essential aspects, including a comprehensive introduction and analysis of the vanilla Bose-Hubbard model and the two-leg Bose-Hubbard ladder under magnetic flux, an in-depth overview of neural-network quantum states tailored for bosonic systems, and a thorough presentation and analysis of the obtained results using neural-network quantum states for these two Bose-Hubbard models.
Open Access
Variational Monte Carlo calculations for Bose-Hubbard model based on projected wavefunctions
(2014) Koç, Fulya
Bose-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].