# name
Mott Insulator-Superﬂuid transition with cold atoms trapped in optical lattice

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Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2021, Tutora: Maria Moreno Cardoner

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We study the superﬂuid-Mott insulator quantum phase transition for ultracold atoms described by the Bose-Hubbard model. We ﬁrst analyse the limiting regimes where only kinetic or interaction energies are present, corresponding to a superﬂuid (delocalized) or a Mott-insulator (localized) state, respectively. Using a variational wave-function, where the diﬀerent sites are decorrelated, and imaginay time propagation we then interpolate between these two cases, and ﬁnd the full phase diagram of the model by analysing the superﬂuid order parameter, and the average and variance of density of particles per site

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Mott Insulator-Superﬂuid transition with cold atoms trapped in optical lattice