BCS-BEC Crossover in the Two-Dimensional Attractive Hubbard Model: Variational Cluster Approach

TL;DR

This study uses the variational cluster approximation to analyze the superconducting ground state in a two-dimensional attractive Hubbard model, revealing a smooth BCS-BEC crossover influenced by quantum fluctuations and energy gain mechanisms.

Contribution

It introduces a detailed analysis of the BCS-BEC crossover in 2D using the variational cluster approach, emphasizing the role of quantum fluctuations and energy contributions.

Findings

Order parameter is suppressed compared to mean-field results due to spatial fluctuations.

Spectra and condensation amplitude show characteristics of Cooper pairs in momentum space.

The pair coherence length indicates a smooth crossover from BCS to BEC regime.

Abstract

We use the variational cluster approximation to study the superconducting ground state in the two-dimensional attractive Hubbard model, putting particular emphasis on the significance of quantum fluctuations of the system. We first show that the order parameter is suppressed in comparison with that obtained using the mean-field theory owing to the effects of spatial fluctuations in two-dimensional systems. We then show that the calculated Bogoliubov quasiparticle spectra and condensation amplitude clearly exhibit the character of Cooper pairs in momentum space and that the pair coherence length $\xi$ evaluated from the condensation amplitude demonstrates a smooth crossover in real space from a weakly paired BCS state ($\xi\gg a$) to a BEC state of tightly bound pairs ($\xi\ll a$), where $a$ is the lattice constant. The calculated kinetic and potential energies in the superconducting and normal ground states indicate that the superconducting state in the weak-coupling region is driven by the gain in potential energy, while that in the strongcoupling region is driven by the gain in kinetic energy.