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We present a large-scale combinatorial-diagrammatic computation of high-ordercontributions to the strong-coupling Kato-Takahashi perturbation series for theHubbard model in high dimensions. The ground-state energy of theMott-insulating phase is determined exactly up to the 15-th order in 1/U. Theperturbation expansion is extrapolated to infinite order and the criticalbehavior is determined using the Domb-Sykes method. We compare the perturbativeresults with two dynamical mean-field theory (DMFT) calculations using aquantum Monte Carlo method and a density-matrix renormalization group method asimpurity solvers. The comparison demonstrates the excellent agreement andaccuracy of both extrapolated strong-coupling perturbation theory and quantumMonte Carlo based DMFT, even close to the critical coupling where the Mottinsulator becomes unstable.

Comparison of computer-algebra strong-coupling perturbation theory and dynamical mean-field theory for the Mott-Hubbard insulator in high dimensions