Reduced-density-matrix analysis of superconducting correlation in two-dimensional and two-chain Hubbard models.

Abstract

We have calculated the largest eigenvalues of the reduced density matrix of the singlet superconducting correlation function and pair-field susceptibility in two-dimensional and two-chain Hubbard models with quantum Monte Carlo methods. A singlet superconducting channel opens upon doping but is otherwise closed at half-filling when U/t=4. The interaction vertex contribution to the largest eigenvalue of the singlet pair-field susceptibility grows with a power law as temperature is decreased. With these two observations, we revise our previous understanding of the interaction vertex in the two-dimensional Hubbard model. We observe that some phases reside in the two-chain Hubbard model. An analysis of the 2${\mathit{k}}_{\mathit{F}}$ charge correlation up to 32\ifmmode\times\else\texttimes\fi{}2 sites suggests that the 2${\mathit{k}}_{\mathit{F}}$ correlation is dominant over the superconducting correlation (0.25\ensuremath{\le}${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$\ensuremath{\le}1.00) in the two-component Luttinger-liquid phase (U/t=2 and ${\mathit{t}}_{\mathit{v}}$/t=1.4). We conclude the reduced-density-matrix analysis discussed here is needed to unveil the nature of Hubbard and related models.