Spin-gapped wave function as normal state in attractive Hubbard model

With the pseudogap in cuprate superconductors in mind, we study an attractive Hubbard model on the square lattice, in which the mechanism of superconductivity undergoes a crossover at |Uco|/t from a BCS type to a Bose-Einstein condensation type, as the interaction strength |U|/t increases. Correspondingly, for |U|>|Uco|, a normatate, realized for T>Tc, is considered to exhibit gapped behavior. We try to construct such a state and study its properties using a variational Monte Carlo method, which treats the local correlation accurately and can connect the weak-and strong-correlation limits continuously. We introduce an intersite correlation factor between antiparallel spins in nearest-neighbor sites, in addition to the onsite (Gutzwiller) projection. This factor brings about a first-order transition from a metal to a spin-gapped phase at |U=|Uc|=W (bandwidth). For |U|>|Uc|, a gap opens in the spin degree of freedom, whereas the charge sector remains gapless. In this phase, conductivity is caused by a hopping of doublons.