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arXiv:0710.1938 · Physical Review A

Stripe formation in fermionic atoms on a two-dimensional optical lattice inside a box trap: Density-matrix renormalization-group studies for the repulsive Hubbard model with open boundary conditions

Masahiko Machida, Masahiko Okumura, S. Yamada

Published Mar 19, 2008• 11 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.77.033619

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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∕tU∕tU∕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∕tU∕tU∕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 an interplay of disorder and correlation in the one-dimensional hole-doped Hubbard-model with disorder (Anderson-Hubbard model) by using the density-matrix renormalization group method. Concentrating on the doped-hole-density profile, we find in a large U/t regime that the clean system exhibits a simple fluidlike behavior whereas finite disorders create locally Mott regions which expand their area with increasing the disorder strength contrary to the conventional sense. We propose that such an anomalous Mott phase formation assisted by disorder is easily observable in atomic Fermi gases by setting up the box-shape trap.
Density matrix renormalization group (DMRG) calculations on four-leg $t\text{\ensuremath{-}}J$ and Hubbard ladders have found a phase exhibiting ``stripes'' at intermediate doping. Such behavior can be viewed as generalized Friedel oscillations, with wavelength equal to the inverse hole density, induced by the open boundary conditions. So far, this phase has not been understood using the conventional weak-coupling bosonization approach. Based on studies of a general bosonization proof, finite size spectrum, an improved analysis of weak-coupling renormalization group equations, and the decoupled two-leg ladder limit, we here find new types of phases of four-leg ladders, which exhibit stripes. They also inevitably exhibit ``bipairing,'' meaning that there is a gap to add one or two electrons (but not four) and that both single electron and electron pair correlation functions decay exponentially, while correlation functions of charge-4 operators exhibit a power-law decay. Whether or not bipairing occurs in the stripe phase found in DMRG is an important open question.
In order to explore a universal feature of atomic Fermi gases loaded on optical lattices, we make a systematic study of the particle density profile for one- and two-dimensional attractive Hubbard models with harmonic potential wells. Using the exact diagonalization scheme and the density-matrix renormalization group technique, we show that fine inhomogeneous zigzag patterns universally emerge in the above models. Theoretical and numerical analyses suggest that these structures originate from an effective repulsive interaction between tightly bound pairs and a breakdown of translational invariance. Furthermore, it is emphasized that the pattern obtained numerically in the two-dimensional model is the checkerboard type, which is very similar to results recently observed in a vortex core of high-Tc{T}_{c}Tc​ cuprate superconductor.
We investigate the properties of fermions trapped in a one-dimensional (1D) optical lattice by using the density-matrix renormalization (DMRG) group method. Owing to a harmonic confinement potential inherent in real experiments, system becomes inhomogeneous structure. Under certain conditions for weak-repulsive interaction, we find that the single-particle excitation spectrum structure changes to band branching and discrete bound-state states as increasing the trap strength. Additionally, we consider the case of strong-repulsive interacting regimes which local density profile show coexist with central Mott-plateau phase with surrounded by metallic regions. As increasing the trap strength, we find the breakdown of 1D Tomonaga-Luttinger (TL) liquid which is alternative to an effective doping into the Mott phase. We will present the various kinds of striking spectra, show the comparison of repulsive interaction case with attractive interaction one.
We study the ground state properties of ultracold fermions trapped in a one-dimensional double-well optical lattice by using the density-matrix renormalization group method. The system is described by an extended Hubbard model with alternating hopping integrals and an external harmonic confining potential. We clarify the characteristic features of the metal–insulator phase transition originating from the double-well structure of the lattices. Several different types of insulating regions coexist when the number of atoms at each site is an integer or a half integer. We found that each insulating phase except for a band insulator exhibits rather large local density fluctuations, reflecting the strong dimerization of atoms within the unit cells of double-well lattices. The phase characteristics are elucidated in detail by investigating the profiles of the local density of atoms, the local density (spin) fluctuations, the double-occupancy probability and the spatially extended sp in correlations.