Pairing correlations in two-dimensional large-size Cu-O clusters: Nonlocal world-line Monte Carlo algorithm

Abstract

A Monte Carlo world-line algorithm for a Cu${\mathrm{O}}_{2}$ plane based on a breakup of the plane into five-site cells, Cu${\mathrm{O}}_{4}$ has been suggested. The algorithm has fast convergency and gives the possibility of investigating the superconducting state symmetry. The calculation of pairing correlation functions was made with an advent of additional imaginary-time slices to the Monte Carlo scheme. The characteristics of a two-dimensional Cu-O cluster with number of sites ${N}_{a}=768$ (16\ifmmode\times\else\texttimes\fi{}16 Cu${\mathrm{O}}_{2}$ cells) were calculated. It has been shown within the chosen interval of parameters of the Emery Hamiltonian (${U}_{d}=6t$, $\ensuremath{\varepsilon}=1\ensuremath{-}3t$, ${U}_{p}=V=0$), temperatures ($T>~0.125t$), and carrier concentrations ($0.7<~x<~1.5$) that (i) the long-range off-diagonal order associated with the superconducting state was not observed in the thermodynamic limit in any pairing channels and (ii) a tendency to divergence in ${s}^{*}$ channels and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ channels, which is noted as the temperature decreases, is due to the antiferromagnetic ordering rather than the superconducting pairing. If the carrier concentration $x$ is equal to 1.0 (undoped dielectric state) the pairing correlations have maximum amplitude and demonstrate clear antiferromagnetic ordering in the copper sublattice, and the characteristic correlation length is close to the earlier-reported antiferromagnetic length.