Guilleumas, MontserratRubio Jiménez, Víctor2025-09-182025-09-182025-01https://hdl.handle.net/2445/223252Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2025, Tutora: Montserrat Guilleumas MorellIn this project, the transition between different quantum phases of ultracold bosonic systems trapped in an optical lattice is studied using the exact diagonalization method. First, the Mott Insulator to Superfluid transition is analyzed. Afterwards, the Density Wave phase is also considered. Specifically, a Julia programming language code is used to find the ground state of a system defined by a Bose-Hubbard Hamiltonian and the phase of this state is determined by means of specific observables derived from the occupation levels.6 p.application/pdfengcc-by-nc-nd (c) Rubio, 2025http://creativecommons.org/licenses/by-nc-nd/3.0/es/Àtom ultrafredXarxa òpticaTreballs de fi de grauUltracold atomOptical latticeBachelor's thesesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess