Stripe Formation and Superfluiditiy Correlation on Two-dimensional Optical Lattice: DMRG Studies for $n$-leg repulsive Hubbard model*

In order to predict strongly-correlated behaviors on two-dimensional (2-D) optical lattice, we employ the parallel density matrix renormalization group (p-DMRG) method and examine 2-D repulsive (square-lattice) Hubbard model. In the presentation, we firstly suggest that box shape trap enables to observe intrinsic properties of the Hubbard model in a fixed doping in contrast to the harmonic trap bringing about wide spatial variations of atom density profiles. Next, we show atomic density profile on 4-leg repulsive Hubbard model with the open boundary condition under the box trap. The variation parameters in the simulation are the doping rate below the half-filling and the repulsive interaction $U/t$. As a result, we find that stripe formations are universal in a low hole doping range and the stripe sensitively changes its structure with variations of $U/t$ and the doping rate. A striking feature is that a stripe by a hole pair turns to one by a bi-hole pair when entering a limited strong $U/t$ range. Furthermore, a systematic calculation reveals that the Hubbard model shows a change from the stripe to the Friedel oscillation with increasing the doping rate.