  The long-studied Hubbard model is one of the simplest models of copper-oxide
superconductors. However, the connection between the model and the experimental
phase diagram is still under debate, in particular regarding the existence and
extent of the $d$-wave superconducting phase. Recent rapid progress in
improving the accuracy of numerical solvers has opened a way to answer this
question reliably. Here, we study the hole-doping concentration ($\delta$)
dependence of the Hubbard model in the ground states on a square lattice at
strong coupling $U/t=10$, for the on-site interaction $U$ and the transfer $t$,
using a variational Monte Carlo method. The method, which combines tensor
network and Lanczos methods on top of Pfaffian wave functions, reveals a rich
phase diagram, in which many orders compete severely and degenerate within the
energy range of 0.01$t$. We have identified distinct phases including a uniform
$d$-wave superconducting phase for $0.17\lesssim \delta \lesssim0.22$ and a
stripe charge/spin ordered phase for $\delta\lesssim0.17$ with the stripe
period depending on $\delta$, together with presumable spatially coexisting
antiferromagnetic and stripe order for $\delta\lesssim0.07$ and coexisting
stripe and $d$-wave superconductivity for $0.07\lesssim\delta\lesssim0.17$. The
present, improved method revealed a wider region of a charge uniform
superconducting phase than the previous studies and shows a qualitative
similarity to the phase diagram of the cuprate superconductors. The
superconducting order parameter is largest at doping of around $\delta=0.17$ in
the ground state, which undergoes phase transitions from an inhomogeneous to a
uniform state.
