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

Abstract

We study 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 to induce 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 $|U_{\mathrm{c}}|\sim W$ ($W$: band width) from a Fermi liquid to a spin-gapped state, which is conductive through hopping of doublons. In the SC state, we confirm by analysis of various quantities that the 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 as the condensation energy, a SC correlation function and the condensate fraction of onsite pairs exhibit behavior of $\sim \exp (-t/|U|)$, as expected from the BCS theory. For $|U|>|U_{\ma{co}}|$, quantities such as the energy gain in the SC transition and superfluid stiffness, which is related to the cost of phase coherence, behave as $\sim t^2/|U|\propto T_{\mathrm{c}}$, as expected in a bosonic scheme. In this regime, the SC transition is induced by a gain in kinetic energy, in contrast with the BCS theory. We refer to the relevance to the pseudogap in cuprate superconductors.

14 pages, 22 figures, submitted to Journal of the Physical Society of Japan

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• Many-Body Physics with Ultracold Gases
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• Observation of pseudogap behavior in a strongly interacting Fermi gas
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• Study of the superconducting order parameter in the negative-$U$ 2D-Hubbard model by grand-canonical twist-averaged boundary conditions
• Drude and Superconducting Weights and Mott Transitions in Variation Theory