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 vertical bar U vertical bar/t increases, a first-order spin-gap transition arises at vertical bar Uc vertical bar similar to 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 vertical bar U-co vertical bar similar to vertical bar U-c vertical bar from a BCS type to a Bose-Einstein condensation (BEC) type, as vertical bar U vertical bar/t increases. For vertical bar U vertical bar < vertical bar U-co vertical bar, quantities such as the condensation energy, a SC correlation function and the condensate fraction of onsite pairs exhibit the behavior of similar to exp(-t/vertical bar U vertical bar), as expected from the BCS theory. For vertical bar U vertical bar > vertical bar U-co vertical bar, quantities such as the energy gain in the SC transition and superfluid stiffness, which is related to the cost of phase coherence, behave as similar to t(2)/vertical bar U vertical bar proportional to T-c, 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.