The thermodynamics of the inhomogeneous one-dimensional repulsive fermionic Hubbard model with parabolic confinement is studied by a density-functional-theory approach, based on Mermin's generalization to finite temperatures. A local-density approximation (LDA), based on exact results for the homogeneous model, is used to approximate the correlation part in the Helmholtz free-energy, comprising the thermodynamic Bethe ansatz LDA (TBALDA). The general presentation of the method is given and some properties of the homogeneous model that are relevant to the DFT approach are analyzed. Extensive comparison between TBALDA and numerical exact diagonalization results for thermodynamic properties of small inhomogeneous chains is discussed. In the remaining, a classical thermodynamic treatment of the confined system is developed with the focus on global properties of large systems. It is observed that, depending on the temperature and specific volume, the system can have its temperature increased under isentropic expansion. Such unusual behavior becomes more pronounced with the increase of the intrasite interaction $U$ and can be understood considering the peculiar behavior of the correlation entropy per site of the Hubbard model around half-filling. A related nonmonotonic variation of the temperature under isentropic change of $U$ is also studied. At the end, the dependence of the double occupancy on temperature and volume per particle is discussed.

• Received 24 July 2014

DOI:https://doi.org/10.1103/PhysRevA.92.013614