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We study properties of normal, superconducting (SC) and CDW states for anattractive Hubbard model on the square lattice, using a variational Monte Carlomethod. In trial wave functions, we introduce an interspinon binding factor,indispensable to induce a spin-gap transition in the normal state, in additionto the onsite attractive and intersite repulsive factors. It is found that, inthe normal state, as the interaction strength $|U|/t$ increases, a first-orderspin-gap transition arises at $|U_{\rm c}|\sim W$ ($W$: band width) from aFermi liquid to a spin-gapped state, which is conductive through hopping ofdoublons. In the SC state, we confirm by analysis of various quantities thatthe mechanism of superconductivity undergoes a smooth crossover at around$|U_{\ma{co}}|\sim |U_{\rm c}|$ from a BCS type to a Bose-Einstein condensation(BEC) type, as $|U|/t$ increases. For $|U|<|U_{\ma{co}}|$, quantities such asthe condensation energy, a SC correlation function and the condensate fractionof onsite pairs exhibit behavior of $\sim \exp(-t/|U|)$, as expected from theBCS theory. For $|U|>|U_{\ma{co}}|$, quantities such as the energy gain in theSC transition and superfluid stiffness, which is related to the cost of phasecoherence, behave as $\sim t^2/|U|\propto T_{\rm c}$, as expected in a bosonicscheme. In this regime, the SC transition is induced by a gain in kineticenergy, in contrast with the BCS theory. We refer to the relevance to thepseudogap in cuprate superconductors.

Variational Monte Carlo Study of Spin-Gapped Normal State and BCS-BEC Crossover in Two-Dimensional Attractive Hubbard Model