Variational monte carlo study of spin-gapped normal state and bcs-bec crossover in two-dimensional attractive hubbard model

We study the properties of normal, superconducting (SC), and CDW states for an attractive Hubbard model on the square lattice, using a variational Monte Carlo method. In trial wave functions, we introduce an interspinon binding factor, indispensable for inducing a spin-gap transition in the normal state, in addition to the onsite attractive and intersite repulsive factors. It is found that, in the normal state, as the interaction strength U=t increases, a first-order spin-gap transition arises at U _c ∼ W (W: bandwidth) from a Fermi liquid to a spin-gapped state, which is conductive as a result of the hopping of doublons. In the SC state, we confirm by the analysis of various quantities that the mechanism of superconductivity undergoes a smooth crossover at approximately Uco∼ U _c from a BCS type to a Bose-Einstein condensation (BEC) type, as U=t increases. For U < Uco, quantities such as the condensation energy, a SC correlation function and the condensate fraction of onsite pairs exhibit the behavior of ∼exp(-t=U), as expected from the BCS theory. For U > Uco, quantities such as the energy gain in the SC transition and superfluid stiffness, which is related to the cost of phase coherence, behave as t2=U / Tc, as expected in a bosonic scheme. In this regime, SC transition is induced by a gain in kinetic energy, in contrast to the BCS theory. We refer to the relevance to the pseudogap in cuprate superconductors.