Numerical Calculations of Phase Diagrams and Thermodynamic Properties of Ultracold Atoms Clusters Localized in Two-Dimensional Optical Lattices

At present, one of the main fields of activity of condensed matter physics is systems of strongly correlated particles, characterized by strong interaction and almost complete absence of analytical description. Experiments for the study of such systems in most cases are extremely costly, complex and expensive, and therefore there is a need for numerical calculation of these objects. The aim of this work is to calculate phase diagrams and thermodynamic properties of clusters of ultracold atoms localized in two-dimensional optical lattices. The interaction of particles in the lattice was described by the Hubbard model, and numerical simulation was performed in the ALPS (Algorithms and Libraries for Physics Simulations) package, designed to simulate highly correlated quantum mechanical systems. The phase diagram calculation program was written in Python programming language. In addition, the dependence of the oscillation period of atoms in optical traps was calculated as a function of the energy of oscillations in the entire energy range of atoms. Phase diagrams were calculated for different parameters of the model, different number of leg ladders (up to 3) and different boundary conditions (open BC and periodic BC – tobleron). As a result, several qualitative theoretical assumptions were tested.