In order to examine the ground state of the single-band Hubbard model from a slightly doped region to an overdoped one, we use the density renormalization group method extended directly to the ladder model and obtain hole profiles with changing the on-site repulsion and the doping ratio. The calculation results in a heavily underdoped region, in which one and two holes (up and down spins) are added, reveal that an attractive interaction works between holes which are confined inside a stripe shape pattern while strong disorders separate the two holes. When doping holes further within an underdoped range, the stripes formed by two holes merge and various stripe structures appear depending on U/t and the doping ratio. The remarkable finding in the underdoped region is a stripe formation composed of 4 holes analytically predicted by Chang and Affleck. On the other hand, in the overdoped range the stripe-like shape becomes very simple, i.e., only a small oscillating charge density profile emerges. These rich features in the underdoped range are relevant to electronic inhomogeneities experimentally observed in high-T c superconductors, while those are directly observable in atomic Fermi gases loaded on optical lattices.
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