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"
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