Exact Diagonalization of the one-dimensional Bose-Hubbard model

Abstract

The Bose-Hubbard model was introduced to describe the behaviour of ultracold bosons trapped in an optical lattice. Such systems present a quantum phase transition of the ground state between two phases: the Mott Insulator and the superfluid phase. We characterise the ground state phases of one-dimensional systems for different lattice sizes with the unit filling. To do so, we use the Exact Diagonalisation method. The computation of the exact ground state energy and eigenvectors enable the study of different relevant physical quantities that will help us portrait such phase transition.