Compressibility and Entropy of One Dimensional Fermions in a combined Harmonic and Periodic Potential

We solve the homogeneous Hubbard model for repulsively interacting fermions using thermodynamic Bethe anzatz method. Treating the harmonic potential in local density approximation, we calculate particle density, various compressibilities, double occupancy, and entropy as a function of temperature and interaction. These quantities show characteristic features that can be used to detect temperature, metal-insulator transition, and coexistence of metallic and insulating phases.