Numerical Calculation of Phase Diagram of the Two-Leg Ladders of Cold Atoms in the Framework of the Attractive-U Hubbard Model

Currently, a large amount of theoretical and experimental research in the field of physics of strongly correlated systems is carried out in the world. Interest in such systems has increased particularly in recent years, when the development of low temperature technology has opened up new opportunities and trends in these studies. In this paper, one-dimensional bound chains of cold atoms interacting by means of atomic spin magnetic moments were considered. On the basis of the Hubbard model with attraction, the numerical calculation of the phase diagram of one, two and three chains of cold atoms was carried out. The calculations were carried out using software of own development in Matlab system and using software package of free distribution of ALPS, managed by commands in Python. Phase diagrams were calculated for different model parameters and different number of chains, a number of qualitative and quantitative theoretical results were tested.