Susceptibilities in the static limit ω→0 are evaluated to show that the superconducting Kosterlitz–Thouless transition exists in the two-dimensional Hubbard model for optimal band parameters. By using quantum Monte Carlo methods, we have examined the size dependence of the spin susceptibility χ( Q ) at half filling and the pair susceptibilities with d - and s -wave symmetries for the repulsive and attractive interactions, respectively. The numerical results for systems of up to 14×14 sites show that the s -wave pair susceptibility scales as χ pair ∼ L 2 for the attractive case, in agreement with previous quantum Monte Carlo studies. The scaling χ pair ∼ L 2 also holds for the d -wave pair susceptibility for the repulsive Hubbard model if we adjust the band parameter t '. Therefore, it is likely that the superconducting Kosterlitz–Thouless transition exists in the two-dimensional repulsive Hubbard model.
The Berezinskii-Kosterlitz-Thouless (BKT) transition is a generic transition describing the loss of coherence in two-dimensional systems and has been invoked, for example, to describe the superconductor-insulator transition in thin films. However, recent experiments have shown that the BKT transition, driven by phase fluctuations, is not sufficient to describe the loss of superconducting order, and amplitude fluctuations must also be taken into account. The standard models that are extensively used to model two-dimensional superconductors are the Hubbard and
XY models. Whereas the
XY model allows only phase fluctuations, the Hubbard model has an extra degree of freedom: amplitude fluctuations. In this paper we compare two Hubbard models with the same critical temperature but with different interactions and deduce the role of the amplitude fluctuations in the superconducting transition. For this purpose, a novel approximation is presented and used. We derive an effective phase-only (
XY) Hamiltonian, incorporating amplitude fluctuations in an explicit temperature dependence of the phase rigidity. We study the relation between amplitude fluctuations and coupling strength. Our results support existing claims about the suppression of phase rigidity due to amplitude fluctuations not present in the
XY model.