Fidelity and superconductivity in two-dimensionalt−Jmodels

Abstract

We compute the ground-state fidelity and various correlations to gauge the competition between different orders in two-dimensional $t\text{\ensuremath{-}}J$-type models. Using exact numerical diagonalization techniques, these quantities are examined for (i) the plain $t\text{\ensuremath{-}}J$ and $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ models, (ii) for the $t\text{\ensuremath{-}}J$ model perturbed by infinite-range $d$-wave or extended-$s$-wave superconductivity inducing terms, and (iii) the $t\text{\ensuremath{-}}J$ model, plain and with a $d$-wave perturbation, in the presence of nonmagnetic quenched disorder. Various properties at low hole doping are contrasted with those at low electron filling. In the clean case, our results are consistent with previous work that concluded that the plain $t\text{\ensuremath{-}}J$ model supports $d$-wave superconductivity. As a consequence of the strong correlations present in the low hole doping regime, we find that the magnitude of the $d$-wave condensate occupation is small even in the presence of large $d$-wave superconductivity inducing terms. In the dirty case, we show the robustness of the ground state in the strongly correlated regime against disorder.