A theoretical model proposed by Hubbard, Kanaori and Gutzwiller for describing the electronic states of transition metal oxides. It consists of the transfer term and on-site Coulomb interaction. Despite its simplicity, its mathematical treatment is rather difficult, allowing exact solution only for very restricted cases, e.g., the one-dimensional system. The model is extensively studied since it exhibits many phases of interest: ferromagnetic, antiferromagnetic, Mott insulator, high-temperature superconducting, etc. Exact diagonalization of small clusters of the model can be done with ALPS, SpinPack, Hphi, etc. By Hphi, calculation of dynamic properties, and finite-temperature calculation is also possible. Calculation by dynamical mean-field theory can be done by ALPS and pyDMFT. Variational Monte Carlo calculation can be done with mVMC.