Superconducting Pair Correlation Function
 
       
 
We have calculated pair correlation functions using the diagonalization Quantum Monte Carlo method [1]. The ground-state wave function is defined as

ψ = e−τ Hψ0,

where H is the Hamiltonian and &psi0 is the initial one-particle state such as the Fermi sea.

We have evaluated pair-correlation functions for the two-dimensional Hubbard model [2]. We have shown that the d-wave pairing correlation function is indeed enhanced slightly for the positive on-site Coulomb interaction U when doping away from the half-filling (Fig.1). The enhancement is very small, but it is important that there is indeed positive enhancement. When the system size becomes large, the d-wave pair correlation function Pd is increased for U > 0 compared to the non-interacting case, while Pd is suppressed for U > 0 when the system size is small.

In the half-filled case, there is, however, no enhancement of pair correlation functions as shown in Fig.2. This may indicate the absence of superconductivity at half-filling.



Fig.1 Pair correlation function as a function of the distance R on 8 × 8 lattice with 54 electrons.



Fig.2 Pair correlation function as a function of the distance R on 8 × 8 lattice at half-filling.



References:

[1] T. Yanagisawa: Physical Review B75 (2007) 224503.
"Quantum Monte Carlo diagonalization method for many-fermion systems"

[2] T. Yanagisawa: New Journal of Physics 15 (2013) 033012.
"Enhanced pair-correlation function in the two-dimensional Hubbard model"


 
 
 
  Condensed Matter Physics: Eectronics and Photonics Research Institute