The Superconducting d-wave Pairing and Antiferromagnetic Order on the Coupled Hubbard Ladders: A Quantum Monte Carlo Study

Using determinant quantum Monte Carlo algorithm, we study the superconducting d-wave pairing and antiferromagnetic order on the coupled Hubbard ladders. With the presence of the next-nearest-neighbor hopping t′=-0.25\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t'=-0.25$$\end{document}, we find that, when the hopping strength among ladders decreases, the d-wave pairing is firstly enhanced and then gets suppressed, showing an optimal hopping inhomogeneity for the d-wave pairing. Without the next-nearest-neighbor hopping, however, the d-wave pairing is suppressed monotonically, i.e., no optimal inhomogeneity exists. We also measure the antiferromagnetic structure factor, which also presents an optimal inhomogeneity with the next-nearest-neighbor hopping t′=-0.25\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t'=-0.25$$\end{document}, and no such optimal inhomogeneity when t′=0.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t'=0.0$$\end{document}. The effect of different temperature, interaction strength, electron density, and lattice size is carefully studied and discussed.