Sentetik manyetik akı altındaki iki-bacaklı Bose-Hubbard merdiveni için sinir-ağ kuantum durumları

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.