To the Hubbard model on a square lattice we add an interaction $W$ that depends upon the square of a near-neighbor hopping. We use zero-temperature quantum Monte Carlo simulations on lattice sizes up to $16\times 16,$ to show that at half-filling and constant value of the Hubbard repulsion, the interaction $W$ triggers a quantum transition between an antiferromagnetic Mott insulator and a $d_{x^2-y^2}$ superconductor. With a combination of finite-temperature quantum Monte Carlo simulations and the maximum entropy method, we study spin and charge degrees of freedom in the superconducting state. We give numerical evidence for the occurrence of a finite-temperature Kosterlitz-Thouless transition to the $d_{x^2-y^2}$ superconducting state. Above and below the Kosterlitz-Thouless transition temperature, $T_{\mathrm{KT}},$ we compute the one-electron density of states $N\left(\omega \right),$ the spin relaxation rate ${1/T}_1,$ as well as the imaginary and real part of the spin susceptibility $\chi (q\to ,\omega ).\mathrm{}$ The spin dynamics are characterized by the vanishing of ${1/T}_1$ and divergence of $\mathrm{Re}\chi (q\to =(\pi ,\pi ),\omega =0\mathrm{})$ in the low-temperature limit. As $T_{\mathrm{KT}}$ is approached $N\left(\omega \right)$ develops a pseudogap feature and below $T_{\mathrm{KT}}\mathrm{Im}\chi (q\to =(\pi ,\pi ),\omega )$ shows a peak at finite frequency.

• Received 10 June 1997

DOI:https://doi.org/10.1103/PhysRevB.56.15001