Competition among various charge-inhomogeneous states and d-wave superconducting state in Hubbard models on square lattices

We study competitions between charge uniform and inhomogeneous states in two-dimensional Hubbard models by using a variational Monte Carlo method. At realistic parameters for cuprate superconductors, emergent effective attraction of carriers generated from repulsive Coulomb interaction leads to charge/spin stripe ground states, which severely compete with uniform superconducting excited states in the energy scale of 10 K for the cuprates. Stripe period increases with decreasing hole doping $\delta$, which agrees with the experiments for La-based cuprates at $\delta$ = 1/8. For lower $\delta$, we find a phase separation. Implications of the emergent attraction for the cuprates are discussed.