The project is devoted to the exact description of the finite temperature properties of the one-dimensional attractive Hubbard model of two-component fermions away from half-filling and in the presence of an external magnetic field. The cases of constant total number of particles and values of the external magnetic field corresponding to the zero temperature critical points are of particular interest. More specifically, we are going to investigate the thermal behavior of the specific heat, magnetization, magnetic susceptibility, etc. As the one-dimensional two-component Hubbard model is an integrable system, we are going to exploit the powerful method of the Quantum Transfer Matrix (QTM) and Non-Linear Integral Equations (NLIE) for obtaining exact results for all thermodynamic functions of the model at finite temperature. With the aid of QTM and NLIE we are going to investigate primarily the following issues: the temperature dependence of the specific heat at critical magnetic fields and away from criticality for a wide range of Hubbard attraction parameter U and filling factor, the thermal and magnetic field dependence of the magnetization in the vicinity of the critical magnetic field. The low filling situation is of eminent interest because of its relevance to ultracold gases. Some comparison with experimental results obtained on optical lattices with spin-polarized Fermi gases is also intended.
DFG Programme
Research Grants
