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We formulate a finite-temperature scheme of the variational clusterapproximation (VCA) particularly suitable for an exact-diagonalization clustersolver. Based on the analytical properties of the single-particle Green'sfunction matrices, we explicitly show the branch-cut structure of logarithm ofthe complex determinant functions appearing in the self-energy-functionaltheory (SFT) and whereby construct an efficient scheme for thefinite-temperature VCA. We first apply the method to explore theantiferromagnetic order in a half-filled Hubbard model by calculating theentropy, specific heat, and single-particle excitation spectrum for differentvalues of on-site Coulomb repulsion $U$ and temperature $T$. We also calculatethe $T$ dependence of the single-particle excitation spectrum in the strongcoupling region, and discuss the overall similarities to and the finedifferences from the spectrum obtained by the spin-density-wave mean-fieldtheory at low temperatures and the Hubbard-I approximation at hightemperatures. On the basis of the thermodynamic properties, we obtain acrossover diagram in the $(U,T)$-plane which separates a Slater-type insulatorand a Mott-type insulator. Next, we demonstrate the finite-temperature schemein the cluster-dynamical-impurity approximation (CDIA) and study theparamagnetic Mott metal-insulator transition in the half-filled Hubbard model.Formulating the finite-temperature CDIA, we first address a subtle issueregarding the treatment of the artificially introduced bath degrees of freedomwhich are absent in the originally considered Hubbard model. We then apply thefinite-temperature CDIA to calculate the finite-temperature phase diagram inthe $(U,T)$-plane. We find that the Mott transition at low temperatures isdiscontinuous, and the coexistence region of the metallic and insulating statespersists down to zero temperature.

physical review. b./physical review. b

Variational cluster approach to thermodynamic properties of interacting  fermions at finite temperatures: A case study of the two-dimensional  single-band Hubbard model at half filling