Hubbard Model in Strong Correlation Regime –Variational Monte-Carlo Studies on Singlet Liquid and Néel State–

The ground state of the Hubbard model on one-dimensional and two-dimensional square lattices is studied with the effective Hamiltonian derived for the strong correlation regime and Gutzwiller-type wave function. The non-half-filled band as well as the half-filled band is discussed. The variational Monte-Carlo method enables us to evaluate the energy for the singlet liquid (resonating-valence-bond state) and for Néel state. The result shows that the stability of the singlet liquid depends on the dimensionality of the system.