Stripe Formation and Superfluiditiy Correlation on Two-dimensional Optical Lattice: DMRG Studies for
n-leg repulsive Hubbard model
We suggest that a box shape trap enables one to observe intrinsic properties of the repulsive Hubbard model in a fixed doping in contrast to the conventional harmonic trap bringing about spatial variations of atom density profiles. In order to predict atomic density profile under the box trap, we apply the directly extended density-matrix renormalization-group method to a four-leg repulsive Hubbard model with the open boundary condition. Consequently, we find that stripe formation is universal in a low-hole-doping range and the stripe sensitively changes its structure with variations of
U∕t and the doping rate. A remarkable change is that a stripe formed by a hole pair turns to one by a bihole 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 like oscillation with increasing the doping rate.
We study repulsive Hubbard and t-J type systems on a square lattice (long believed to capture certain quintessential aspects of the high temperature superconductors). These models (alongside the parent compounds of the high temperature superconductors) are antiferromagnetic in the absence of hole doping. As we illustrate, a unifying underlying principle for the dynamics of holes introduced by doping rationalizes the emergence of nonuniform electronic structures- "stripes" and possible pairing tendencies therein. Specifically, our analysis invokes the following (numerically verified) sublattice parity principle: a strong antiferromagnetic background forces injected holes to hop in steps of two such that they always remain on the same sub lattice. When applied to a domain wall in an antiferromagnet, this simple principle naturally gives rise to (bond centered) stripes. We demonstrate that the holes are self-consistently localized on stripes. Extending this picture, we then show that the holes on a stripe favor the formation of pairs on neighboring rungs or sites. Throughout this work much emphasis is placed on the problem of a two leg ladder immersed in a staggered magnetic field. Although we will focus on the square lattice, our considerations may be extended to similar electronic structures appearing in other models on bipartite lattices when these exhibit antiferromagnetic correlations with an underlying sublattice structure.