Charge and spin structures of a superconductor in the proximity of an antiferromagnetic Mott insulator

To the Hubbard model on a square lattice we add an interaction (Formula presented) that depends upon the square of a near-neighbor hopping. We use zero-temperature quantum Monte Carlo simulations on lattice sizes up to (Formula presented) to show that at half-filling and constant value of the Hubbard repulsion, the interaction (Formula presented) triggers a quantum transition between an antiferromagnetic Mott insulator and a (Formula presented) 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 (Formula presented) superconducting state. Above and below the Kosterlitz-Thouless transition temperature, (Formula presented) we compute the one-electron density of states (Formula presented) the spin relaxation rate (Formula presented) as well as the imaginary and real part of the spin susceptibility (Formula presented) The spin dynamics are characterized by the vanishing of (Formula presented) and divergence of (Formula presented) in the low-temperature limit. As (Formula presented) is approached (Formula presented) develops a pseudogap feature and below (Formula presented) shows a peak at finite frequency.