Thermodynamics of the two-level Richardson model

The two-level version of the Richardson model presents a unique possibility to calculate numerically exactly thermodynamic properties of the system it describes. The point is that all energies and the degeneracies of the many-body system can be easily calculated. The energies are given by the eigenvalues of the small (of order of N x N, where 2N is a number of electrons in the system) tridiagonal matrices. Here we numerically obtain a complete spectrum of the interacting two-level model and calculate the specific heat and the pairing energy of the small system at finite temperatures.